## Powers & Sum Digits – Num3ers from 2 to 99 [Part 1]

Part One: From the numbers 2 to 99
Next : Numbers from 100 to 200

I’ve checked all the numbers from 2 to 99 raised to the power k, with k = 1, 2, 3, …, 20

2^6 = 64 = (6 – 4)^6
2^9 = 512 = (5 – 1 – 2)^9
2^11 = 2048 = (-2 + 0 – 4 + 8)^11
where -2 + 0 – 4 + 8 = 2
2^13 = 8192 = (-8-1+9+2)^13
where (-8) – 1 + 9 + 2 = 2
2^14 = 16384 = (-1-6-3+8+4)^14
where (-1) – 6 – 3 + 8 + 4 = 2
2^15 = 32768 = (-3-2-7+6+8)^15
where (-3) – 2 – 7 + 6 + 8 = 2
2^16 = 65536     N/A
2^17 = 131072     N/A
2^18 = 262144     N/A
2^19 = 524288     N/A
2^20 = 1048576     N/A

3^5 = 243 = (2 + 4 – 3)^5

4^k,    k=1, 2, …, 20     N/A

5^5 = 3125 = (3 – 1 – 2 + 5)^5
where 3 – 1 – 2 + 5 = 5

6^4 = 1,296 = (1 + 2 + 96)^4

15^5 = 759,375 = (7–5+9–3+7)^5
where 7 – 5 + 9 – 3 + 7 = 15

17^2 = 289     N/A
17^3 = 4913 = (4+9+1+3)^3
where 4 + 9 + 1 + 3 = 17
17^4 = 83,521 = (8+3+5+2–1)^4
where 8 + 3 + 5 + 2 – 1 = 17
17^5 = 1419857     N/A
17^6 = 24,137,569 = (24–13+75–69)^6
where 24 – 13 + 75 – 69 = 17
17^7 = 410338673     N/A
17^8 = 6975757441     N/A
17^9 = 118587876497     N/A

18^1 = 18 = 1 || 8 and 18 = 2*(1+8)
18^2 = 324     N/A
18^3 = 5832 = (5+8+3+2)^3
where 5 + 8 + 3 + 2 = 18
18^4 = 104976     N/A
18^5 = 1889568     N/A
18^6 = 34,012,224 = (3+4+0+1+2+2+2+4)^6
where 3 + 4 + 0 + 1 + 2 + 2 + 2 + 4 = 18
18^7 = 612,220,032 = (6+1+2+2+2+0+0+3+2)^7
where 6 + 1 + 2 + 2 + 2 + 0 + 0 + 3 + 2 = 18
18^8 = 11019960576       N/A
18^9 = 198359290368       N/A

22^2 = 484      N/A
22^3 = 10648      N/A
22^4 = 234,256 = (2+3+4+2+5+6)^4
where 2 + 3 + 4 + 2 + 5 + 6 = 22
22^5 = 5153632      N/A
22^6 = 113,379,904 = (11+3–3+7–9+9–0+4)^6
where 11 + 3 – 3 + 7 – 9 + 9 – 0 + 4 = 22
22^7 = 2,494,357,888 = (24–9+4–3+5–7+8–8+8)^7
where 24 – 9 + 4 – 3 + 5 – 7 + 8 – 8 + 8 = 22
22^8 = 54875873536      N/A
22^9 = 1207269217792      N/A

30^k,    k=1, 2, …, 20    N/A

31^7 = 27,512,614,111 = (2+7+5+1+2+6+1+4+1+1+1)^7
where 2 + 7 + 5 + 1 + 2 + 6 + 1 + 4 + 1 + 1 + 1 = 31

32^k,    k=1, 2, …, 20    N/A
33^k,    k=1, 2, …, 20    N/A

34^4 = 1,336,336 = (13+3+6+3+3+6)^4 = (01+33–6+3–3+6)^4
where 13 + 3 + 6 + 3 + 3 + 6 = 34 = 1 + 33 – 6 + 3 – 3 + 6
34^7 = 52,523,350,144 = (5+2+5+2+3+3+5+0+1+4+4)^4
where 5 + 2 + 5 + 2 + 3 + 3 + 5 + 0 + 1 + 4 + 4 = 34

35^5 = 52,521,875 = (5+2+5+2+1+8+7+5)^5
where 5 + 2 + 5 + 2 + 1 + 8 + 7 + 5 = 35

36^2 = 1,296 = (1+29+6)^2
where 1 + 29 + 6 = 36
36^4 = 1,679,616 = (1+6+7+9+6+1+6)^4
where 1 + 6 + 7 + 9 + 6 + 1 + 6 = 36
36^5 = 60,466,176 = (6+0+4+6+6+1+7+6)^5
where 6 + 0 + 4 + 6 + 6 + 1 + 7 + 6 = 36

37^4 = 1,874,161 = (18+7+4+1+6+1)^4
where 18 + 7 + 4 + 1 + 6 + 1 = 37

38^k,    k=1, 2, …, 20    N/A
39^k,    k=1, 2, …, 20    N/A
40^k,    k=1, 2, …, 20    N/A
41^k,    k=1, 2, …, 20    N/A
42^k,    k=1, 2, …, 20    N/A

43^4 = 3,418,801 = (–03–41+88–01)^4
where (-3) – 41 + 88 – 1 = 43
43^7 = 271,818,611,107 = (2+7+1+8+1+8+6+1+1+1+0+7)^7
where 2 + 7 + 1 + 8 + 1 + 8 + 6 + 1 + 1 + 1 + 0 + 7 = 43

44^2 = 1,936 = (–1+9+36)^2
where (-1) + 9 + 36 = 44
44^5 = 164,916,224 = (1+6+4+9+16+2+2+4)^5
where 1 + 6 + 4 + 9 + 16 + 2 + 2 + 4 = 44
44^6 = 7,256,313,856 = (7+2+5+6+3–1+3+8+5+6)^6
where 7 + 2 + 5 + 6 + 3 – 1 + 3 + 8 + 5 + 6 = 44

45^2 = 2025 = (20+25)^2
where 20 + 25 = 45
45^3 = 91,125 = (09+11+25)^3
where 9 + 11 + 25 = 45
45^4 = 4,100,625 = (04+10+06+25)^4
where 4 + 10 + 6 + 25 = 45
45^5 = 184,528,125 = (1+8+4+5+2+8+12+5)^5
where 1 + 8 + 4 + 5 + 2 + 8 + 12 + 5 = 45
45^6 = 8,303,765,625 = (8+3+0+3+7+6+5+6+2+5)^6
where 8 + 3 + 0 + 3 + 7 + 6 + 5 + 6 + 2 + 5 = 45

46^2 = 2116     N/A
46^3 = 97336     N/A
46^4 = 4477456     N/A
46^5 = 205,962,976 = (2+0+5+9+6+2+9+7+6)^5
where 2 + 0 + 5 + 9 + 6 + 2 + 9 + 7 + 6 = 46
46^6 = 9474296896     N/A
46^7 = 435817657216     N/A
46^8 = 20,047,612,231,936 = (2+0+0+4+7+6+1+2+2+3+1+9+3+6)^8
where 2 + 0 + 0 + 4 + 7 + 6 + 1 + 2 + 2 + 3 + 1 + 9 + 3 + 6 = 46
46^9 = 922190162669056     N/A
46^10 = 42420747482776576     N/A

47^k,    k=1, 2, …, 20    N/A
48^k,    k=1, 2, …, 20    N/A
49^k,    k=1, 2, …, 20    N/A

50^k,    k=1, 2, …, 20    N/A

51^3 = 132,651 = (–13–2+65+1)^3 = (–1–3–2+6+51)^3
where (-13) – 2 + 65 + 1 = 51 = (-1) – 3 – 2 + 6 + 51

52^4 = 7,311,616 = (7+31+1+6+1+6)^4
where 7 + 31 + 1 + 6 + 1 + 6 = 52

53^5 = 418,195,493 = (4+18+1+9+5+4+9+3)^5
where 4 + 18 + 1 + 9 + 5 + 4 + 9 + 3 = 53

53^6 = 22164361129    N/A

53^7 = 1,174,711,139,837 = (1+1+7+4+7+1+1+1+3+9+8+3+7)^7
where 1 + 1 + 7 + 4 + 7 + 1 + 1 + 1 + 3 + 9 + 8 + 3 + 7 = 53

54^4 = 8,503,056 = (8+5+0+30+5+6)^4
where 8 + 5 + 0 + 30 + 5 + 6 = 54
54^5 = 459,165,024 = (4+5+9+1+6+5+0+24)^5
where 4 + 5 + 9 + 1 + 6 + 5 + 0 + 24 = 54
54^6 = 24,794,911,296 = (2+4+7+9+4+9+1+1+2+9+6)^6
where 2 + 4 + 7 + 9 + 4 + 9 + 1 + 1 + 2 + 9 + 6 = 54
54^7 = 1338925209984    N/A
54^8 = 72,301,961,339,136 = (7+2+3+0+1+9+6+1+3+3+9+1+3+6)^8
where 7 + 2 + 3 + 0 + 1 + 9 + 6 + 1 + 3 + 3 + 9 + 1 + 3 + 6 = 54
54^9 = 3,904,305,912,313,344 = (3+9+0+4+3+0+5+9+1+2+3+1+3+3+4+4)^9
where 3 + 9 + 0 + 4 + 3 + 0 + 5 + 9 + 1 + 2 + 3 + 1 + 3 + 3 + 4 + 4 = 54

54^10 = 210832519264920576    N/A

55^2 = 3,025 = (30+25)^2
where 30 + 25 = 55
55^3 = 166,375 = (1+6+6+37+5)^3
where 1 + 6 + 6 + 37 + 5 = 55
55^4 = 9,150,625 = (09+15+06+25)^4
where 9 + 15 + 6 + 25 = 55
55^5 = 503,284,375 = (5+0+3+28+4+3+5+7)^5
where 5 + 0 + 3 + 28 + 4 + 3 + 5 + 7 = 55
55^6 = 27680640625    N/A
55^7 = 1,522,435,234,375 = (15+2+2+4+3+5+2+3+4+3+7+5)^7
where 15 + 2 + 2 + 4 + 3 + 5 + 2 + 3 + 4 + 3 + 7 + 5 = 55
55^8 = 83733937890625    N/A
55^9 = 4605366583984375    N/A
55^10 = 253295162119140625    N/A

56^k,    k=1, 2, …, 20    N/A
57^k,    k=1, 2, …, 20    N/A

58^2 = 3364 = (–3–3+64)^2
where (-3) – 3 + 64 = 58
58^3 = 195,112 = (+19+51–12)^3
where 19 + 51 – 12 = 58
58^4 = 11,316,496 = (1+1+31+6+4+9+6)^4
where 1 + 1 + 31 + 6 + 4 + 9 + 6 = 58
58^5 = 656356768    N/A
58^6 = 38068692544    N/A
58^7 = 2,207,984,167,552 = (2+2+0+7+9+8+4+1+6+7+5+5+2)^7
where 2 + 2 + 0 + 7 + 9 + 8 + 4 + 1 + 6 + 7 + 5 + 5 + 2 = 58
58^8 = 128063081718016    N/A
58^9 = 7427658739644928    N/A
58^10 = 430804206899405824    N/A

59^k,    k = 1, 2, 3, …, 20    N/A

60^k,    k=1, 2, …, 20    N/A

61^4 = 13,845,841 = (1+38+4+5+8+4+1)^4
where 1 + 38 + 4 + 5 + 8 + 4 + 1 = 61

62^3 = 238,328 = (23+8+3+28)^3
where 23 + 8 + 3 + 28 = 62
62^4 = 14776336    N/A
62^5 = 916,132,832 = (9+1+6+1+3+2+8+32)^5
where 9 + 1 + 6 + 1 + 3 + 2 + 8 + 32 = 62

63^2 = 3969 = (3–9+69)^2
where 3 – 9 + 69 = 63
63^4 = 15,752,961 = (15+7+5+29+6+1)^4
where 15 + 7 + 5 + 29 + 6 + 1 = 63
63^8 = 24,815,578,026,7521 = (2+4+8+1+5+5+7+8+0+2+6+7+5+2+1)^8
where 2 + 4 + 8 + 1 + 5 + 5 + 7 + 8 + 0 + 2 + 6 + 7 + 5 + 2 + 1 = 63

64^5 = 1,073,741,824 = (10+7+3+7+4+1+8+24)^5
where 10 + 7 + 3 + 7 + 4 + 1 + 8 + 24 = 64
64^6 = 68,719,476,736 = (6+8+7+1+9+4+7+6+7+3+6)^6
where 6 + 8 + 7 + 1 + 9 + 4 + 7 + 6 + 7 + 3 + 6 = 64

65^k,    k=1, 2, …, 20    N/A
66^k,    k=1, 2, …, 20    N/A

67^4 = 20,151,121 = (20+15+11+21)^4
where 20 + 15 + 11 + 21 = 67

68^7 = 6,722,988,818,432 = (6+7+2+2+9+8+8+8+1+8+4+3+2)^7
where 6 + 7 + 2 + 2 + 9 + 8 + 8 + 8 + 1 + 8 + 4 + 3 + 2 = 68

69^k,    k=1, 2, …, 20    N/A

70^k,    k=1, 2, …, 20    N/A

71^2 = 5041       N/A
71^3 = 357,911 = (3+57+9+1+1)^3
where 3 + 57 + 9 + 1 + 1 = 71
71^4 = 25411681       N/A
71^5 = 1804229351       N/A
71^6 = 128100283921       N/A
71^7 = 9095120158391       N/A
71^8 = 645753531245761       N/A
71^9 = 45,848,500,718,449,031 = (4+5+8+4+8+5+0+0+7+1+8+4+4+9+0+3+1)^9
where 4 + 5 + 8 + 4 + 8 + 5 + 0 + 0 + 7 + 1 + 8 + 4 + 4 + 9 + 0 + 3 + 1 = 71
71^10 = 3255243551009881201       N/A

72^2 = 5184     N/A
72^3 = 373,248 = (37+3+24+8)^3
where 37 + 3 + 24 + 8 = 72
72^4 = 26,873,856 = (2+6+8+7+38+5+6)^4
where 2 + 6 + 8 + 7 + 38 + 5 + 6 = 72
72^5 = 1,934,917,632 = (1+9+3+4+9+1+7+6+32)^5
where 1 + 9 + 3 + 4 + 9 + 1 + 7 + 6 + 32 = 72
72^6 = 139,314,069,504 = (1+39+3+1+4+0+6+9+5+0+4)^6
where 1 + 39 + 3 + 1 + 4 + 0 + 6 + 9 + 5 + 0 + 4 = 72
72^7 = 10,030,613,004,288 = (1+0+0+3+0+6+1+3+0+0+42+8+8)^7
1 + 0 + 0 + 3 + 0 + 6 + 1 + 3 + 0 + 0 + 42 + 8 + 8 = 72
72^8 = 722,204,136,308,736 = (7+2+2+20+4+1+3+6+3+0+8+7+3+6)^8
where 7 + 2 + 2 + 20 + 4 + 1 + 3 + 6 + 3 + 0 + 8 + 7 + 3 + 6 = 72
72^9 = 51998697814228992
where 5 + 1 + 9 + 9 + 8 + 6 + 9 + 7 + 8 + 1 + 4 + 2 + 2 + 8 + 9 + 9 + 2 = 99    N/A

73^4 = 28,398,241 = (2+8+3+9+8+2+41)^4
where 2 + 8 + 3 + 9 + 8 + 2 + 41 = 73

74^k,    k=1, 2,…, 20     N/A
75^k,    k=1, 2,…, 20     N/A
76^k,    k=1, 2,…, 20     N/A

77^3 = 456,533 = (–456+533)^3
where (-456) + 533 = 77
77^4 = 35,153,041 = (–035+153–041)^4
where (-35) + 153 – 41 = 77
77^5 = 2,706,784,157 = (–002+706–784+157)^5
where (-2) + 706 – 784 + 157 = 77
77^6 = 208,422,380,089 = (208–422+380–089)^6
where 208 – 422 + 380 – 89 = 77
77^7 = 16,048,523,266,853
where 016–048+523–266+853 = 1,078 = –001+078 = 77
77^8 = 1,235,736,291,547,681 = (1–235+736–291+547–681)^8
where 1 – 235 + 736 – 291 + 547 – 681 = 77
77^9 = 95,151,694,449,171,437 = (–095+151–694+449–171+437)^9
where (-95) + 151 – 694 + 449 – 171 + 437 = 77

78^2 = 6084 = (–006+084)^2
where (-6) + 84 = 78
78^3 = 474552 = (–474+552)^3
where (-474) + 552 = 78
78^4 = 37,015,056 = (037–015+056)^4
where 37 – 15 + 56 = 78
78^6 = 225,199,600,704 = (–225+199–600+704)^6
where (-225) + 199 – 600 + 704 = 78
78^7 = 17,565,568,854,912 = (017–565+568–854+912)^7
where 17 – 565 + 568 – 854 + 912 = 78
78^8 = 1,370,114,370,683,136 = (–001+370–114+370–683+136)^8
where (-1) + 370 – 114 + 370 – 683 + 136 = 78
78^9 = 106868920913284608     N/A
78^10 = 8,335,775,831,236,199,424 = (008–335+775–831+236–199+424)^10
where 8 – 335 + 775 – 831 + 236 – 199 + 424 = 78
78^11 = 650,190,514,836,423,555,072 = (650–190+514–836+423–555+072)^11
where 650 – 190 + 514 – 836 + 423 – 555 + 72 = 78
78^12 = 50,714,860,157,241,037,295,616
= (–050+714–860+157–241+037–295+616)^12
where (-50) + 714 – 860 + 157 – 241 + 37 – 295 + 616 = 78
78^13 = 3,955,759,092,264,800,909,058,048
= (003–955+759–092+264–800+909–058+048)^13
where 3 – 955 + 759 – 92 + 264 – 800 + 909 – 58 + 48 = 78

90^k,    k=1, 2,…, 20     N/A

91^2 = 8281 = (82+8+1)^2 = (8+2+81)^2
where 82 + 8 + 1 = 91 = 8 + 2 + 81    and 19 = 8 + 2 + 8 + 1

92^4 = 71,639,296 = (–7+1+6–3+92+9–6)^4
where (-7) + 1 + 6 – 3 + 92 + 9 – 6 = 92

93^3 = 804,357 = (80+4–3+5+7)^3
where 80 + 4 – 3 + 5 + 7 = 93
93^4 = 74,805,201 = (7+4+80+5–2–0–1)^4
where 7 + 4 + 80 + 5 – 2 – 0 – 1 = 93
93^5 = 7,339,040,224 = (73+3+9+0+4+0+2–2+4)^5 = (73–3–9–0+40–2–2–4)^5
where 73 + 3 + 9 + 0 + 4 + 0 + 2 – 2 + 4 = 93 = 73 – 3 – 9 – 0 + 40 – 2 – 2 – 4

94^3 = 830,584 = (8–3+0+5+84)^3
where 8 – 3 + 0 + 5 + 84 = 94
94^10 = 53,861,511,409,489,970,176 =
= (5+3+8+6+1+5+1+1+4+0+9+4+8+9+9+7+0+1+7+6)^10
where 5 + 3 + 8 + 6 + 1 + 5 + 1 + 1 + 4 + 0 + 9 + 4 + 8 + 9 + 9 + 7 + 0 + 1 + 7 + 6 = 94

95^4 = 81,450,625 = (81+45–06–25)^4
where 81 + 45 – 6 – 25 = 95

96^3 = 884,736 = (88+4+7+3–6)^3
where 88 + 4 + 7 + 3 – 6 = 96

97^3 = 912,673 = (91+2–6+7+3)^3
where 91 + 2 – 6 + 7 + 3 = 97
97^10 = 73,742,412,689,492,826,049 =
= (7+3+7+4+2+4+1+2+6+8+9+4+9+2+8+2+6+0+4+9)^10
where 7 + 3 + 7 + 4 + 2 + 4 + 1 + 2 + 6 + 8 + 9 + 4 + 9 + 2 + 8 + 2 + 6 + 0 + 4 + 9 = 97

98^3 = 941,192 = (94+11–9+2)^3
where 94 + 11 – 9 + 2 = 98

99^2 = 9801 = (98+01)^2
where 98 + 01 = 99
99^3 = 970,299 = (9+70+2+9+9)^3
where 9 + 70 + 2 + 9 + 9 = 99
99^4 = 96059601     N/A
99^5 = 9,509,900,499 = (9+50+9+9+0+0+4+9+9)^5
where 9 + 50 + 9 + 9 + 0 + 0 + 4 + 9 + 9 = 99
99^6 = 941,480,149,401 = (9+4+14+8+0+14+9+40+1)^6
where 9 + 4 + 14 + 8 + 0 + 14 + 9 + 40 + 1 = 99
99^7 = 93,206,534,790,699 = (9+32+0+6+5+3+4+7+9+0+6+9+9)^7
where 9 + 32 + 0 + 6 + 5 + 3 + 4 + 7 + 9 + 0 + 6 + 9 + 9 = 99
99^8 = 9227446944279201     N/A
99^9 = 913517247483640899     N/A

math grad - Interest: Number theory
This entry was posted in Math Beauty and tagged , . Bookmark the permalink.

### 7 Responses to Powers & Sum Digits – Num3ers from 2 to 99 [Part 1]

1. I truly enjoy reading through on this web site, it has wonderful posts. “The living is a species of the dead and not a very attractive one.” by Friedrich Wilhelm Nietzsche.

• benvitalis says:

Thanks. I’m glad you enjoyed it.

2. Paul says:

Hope you don’t mind, I’ve re-calculated some of them again and filled in some N/A ones. I will attempt to do some of the larger numbers at a later date, but for now here are my versions of the numbers 2 to 6 each raised to the power 1 to 20. I have made two lists ones starting with a negative first number and a second list starting with a positive first number, some numbers can be reached both ways so the list is sorted into number order. The format is:-
number, power, n^p, and the method to construct that number using the digits in order.

{2,1,2,2}
{2,6,64,6-4}
{2,9,512,5-1-2}
{2,11,2048,-2+0-4+8}
{2,13,8192,-8-1+9+2}
{2,13,8192,8+1-9+2}
{2,14,16384,-1-6-3+8+4}
{2,14,16384,1-6+3+8-4}
{2,15,32768,-3-2-7+6+8}
{2,17,131072,-13+10+7-2}
{2,17,131072,1-3-1+07-2}
{2,20,1048576,-10-4+8-5+7+6}
{2,20,1048576,10+4-8-5+7-6}

{3,1,3,3}
{3,5,243,2+4-3}
{3,9,19683,-1+9+6-8-3}
{3,9,19683,1-9+6+8-3}
{3,11,177147,-1+7+7+1-4-7}
{3,11,177147,17+7-14-7}
{3,12,531441,-5-3+14-4+1}
{3,13,1594323,-1+5-9+4+3-2+3}
{3,13,1594323,1+5+9-4-3-2-3}
{3,14,4782969,-47-8-2-9+69}
{3,14,4782969,4-7-8+29-6-9}
{3,15,14348907,-14+3+4+8+9+0-7}
{3,15,14348907,14+3-4-8-9+07}
{3,16,43046721,-4+3+04+6-7+2-1}
{3,16,43046721,43+0-46+7-2+1}
{3,17,129140163,-129+140+1-6-3}
{3,17,129140163,12+9-14+0-1-6+3}
{3,18,387420489,-38+74-20+4-8-9}
{3,18,387420489,3+87+4+2+0-4-89}
{3,19,1162261467,-11+62-2+6+1-46-7}
{3,19,1162261467,11+62-2-6+1+4-67}
{3,20,3486784401,-34+8-6+78-44+01}
{3,20,3486784401,34+8-6-78+44+01}

{4,1,4,4}
{4,5,1024,10-2-4}
{4,7,16384,-1+6+3-8+4}
{4,7,16384,1-6-3+8+4}
{4,9,262144,-2-6+2+14-4}
{4,9,262144,2-6-2+14-4}
{4,10,1048576,-10+4-8+5+7+6}
{4,10,1048576,10+4+8-5-7-6}
{4,11,4194304,-4+19-4-3+0-4}
{4,12,16777216,-16+7-7-7+21+6}
{4,12,16777216,16+7-7-7+2-1-6}
{4,13,67108864,-6+7+1+08-8+6-4}
{4,13,67108864,67+1+08-8-64}
{4,14,268435456,-26+84+3-5+4-56}
{4,14,268435456,26-84-3+54+5+6}
{4,15,1073741824,-10+73-74+1+8+2+4}
{4,15,1073741824,10+73-74+1-8-2+4}
{4,16,4294967296,-42+9+49-6+7+2-9-6}
{4,16,4294967296,42+9-49-6+7-2+9-6}
{4,17,17179869184,-171+79+8-6+9+1+84}
{4,17,17179869184,171+7-9-86-91+8+4}
{4,18,68719476736,-687-1+9-47-6+736}
{4,18,68719476736,687-19-4+76-736}
{4,19,274877906944,-27+48+7+7-90+6+9+44}
{4,19,274877906944,274-87-79+0-6-94-4}
{4,20,1099511627776,-1099+5+1162+7-77+6}
{4,20,1099511627776,1099+5-1162-7-7+76}

{5,1,5,5}
{5,5,3125,-3+1+2+5}
{5,5,3125,3-1-2+5}
{5,6,15625,-1+5-6+2+5}
{5,6,15625,1+5+6-2-5}
{5,7,78125,-7+8+1-2+5}
{5,7,78125,7-8-1+2+5}
{5,8,390625,-3+9+06-2-5}
{5,9,1953125,-19-5+3+1+25}
{5,9,1953125,19-5-3+1-2-5}
{5,10,9765625,-9+76+5-62-5}
{5,10,9765625,9-76+5+62+5}
{5,11,48828125,-48+8+28+12+5}
{5,11,48828125,48-8-28-12+5}
{5,12,244140625,-24-4+14+0-6+25}
{5,12,244140625,24+4-14+0-6+2-5}
{5,13,1220703125,-12+20+7+0-3-12+5}
{5,13,1220703125,12+20+7+0-31+2-5}
{5,14,6103515625,-610-3+51+562+5}
{5,14,6103515625,610+35-15-625}
{5,15,30517578125,-30+51+75-7-81+2-5}
{5,15,30517578125,30+51-75-7+8+1+2-5}
{5,16,152587890625,-1525+8+7+890+625}
{5,16,152587890625,152+5-8-78-9+0-62+5}
{5,17,762939453125,-76+29+39+4+5-3+12-5}
{5,17,762939453125,762-939+4+53+125}
{5,18,3814697265625,-381+469-7+2-65-6-2-5}
{5,18,3814697265625,381-469+7+2+65-6+25}
{5,19,19073486328125,-190+734-86-328-125}
{5,19,19073486328125,190+7+3+48+63-281-25}
{5,20,95367431640625,-953-6+743+164+062-5}
{5,20,95367431640625,953+6+743-1640-62+5}

{6,1,6,6}
{6,4,1296,1+2+9-6}
{6,6,46656,-4+66-56}
{6,7,279936,-2-79+93-6}
{6,7,279936,27-9-9+3-6}
{6,8,1679616,-1+6-7+9+6-1-6}
{6,8,1679616,1+6+7-9+6+1-6}
{6,9,10077696,-1+00-7-7+6+9+6}
{6,9,10077696,1+007+7+6-9-6}
{6,10,60466176,-60+46+6+1+7+6}
{6,10,60466176,60-46+6-1-7-6}
{6,11,362797056,-36+27+9+7+05-6}
{6,11,362797056,36-27-9+7+05-6}
{6,12,2176782336,-21+76-78+2+33-6}
{6,12,2176782336,21+76-78+23-36}
{6,13,13060694016,-13+060+6+9-40-16}
{6,13,13060694016,13+06+0-69+40+16}
{6,14,78364164096,-78+36+41+6+4+0-9+6}
{6,14,78364164096,78+36-41-64+0-9+6}
{6,15,470184984576,-470+18-4-9+8+457+6}
{6,15,470184984576,470+1+84-98-457+6}
{6,16,2821109907456,-28+21+1+09-9+07+4-5+6}
{6,16,2821109907456,282-110+9-90-74-5-6}
{6,17,16926659444736,-169+266+5-94+4+4-7+3-6}
{6,17,16926659444736,169+266-5-9-444-7+36}
{6,18,101559956668416,-1015+599-56-6+68+416}
{6,18,101559956668416,1015+59-956-6-6-84-16}
{6,19,609359740010496,-609+35+9+74+001+0496}
{6,19,609359740010496,609+35+9-740+01+0-4+96}
{6,20,3656158440062976,-3656+1-58+4+4006-297+6}
{6,20,3656158440062976,3656-1+58-4-4006+297+6}

Paul.

3. Paul says:

I have uploaded a txt file containing the digits 2 to 99 with not a ‘perfect’ solution in that some of the numbers have leading zeros like 007 etc. I would say that there is an almost certainty (as the mantissa gets larger) that there will be a perfect solution for all entries.