Comments for Fun With Num3ers http://benvitalenum3ers.wordpress.com Just another WordPress.com site Tue, 21 May 2013 20:24:43 +0000 hourly 1 http://wordpress.com/ Comment on Using Primes 2,3,5,7 only once to make 1-100 by benvitalis http://benvitalenum3ers.wordpress.com/2013/05/21/using-primes-2357-only-once-to-make-1-100/#comment-8990 Tue, 21 May 2013 20:24:43 +0000 http://benvitalenum3ers.wordpress.com/?p=11728#comment-8990 Very Nice!

]]> Comment on Using Primes 2,3,5,7 only once to make 1-100 by claudio http://benvitalenum3ers.wordpress.com/2013/05/21/using-primes-2357-only-once-to-make-1-100/#comment-8989 Tue, 21 May 2013 19:56:57 +0000 http://benvitalenum3ers.wordpress.com/?p=11728#comment-8989 http://www.milefoot.com/math/integermania/first4primes-1.htm

]]> Comment on Non-palindrome multiplied by its reverse is a square by David @InfinitelyManic http://benvitalenum3ers.wordpress.com/2013/05/21/non-palindrome-multiplied-by-its-reverse-is-a-square/#comment-8987 Tue, 21 May 2013 16:08:58 +0000 http://benvitalenum3ers.wordpress.com/?p=11722#comment-8987 # !/usr/bin/python3
# David
# Non-palindrome multiplied by its reverse is a square

from custom_functions import *

for n in range(1,10**5):
r = int(str(n)[::-1])
p = n * r
sr = int(math.sqrt(p))
if (
isPalin(n) is False and
isSquare(n) is False and
isSquare(p) is True and
str(n).endswith(’0′) is False
):
print(‘{0} * {1} = {2} = {3}^2 is a perfect square’.format(n,r,p,sr))

## some solutions where n does not end with zero (0)
288 * 882 = 254016 = 504^2 is a perfect square
528 * 825 = 435600 = 660^2 is a perfect square
768 * 867 = 665856 = 816^2 is a perfect square
825 * 528 = 435600 = 660^2 is a perfect square
867 * 768 = 665856 = 816^2 is a perfect square
882 * 288 = 254016 = 504^2 is a perfect square
1584 * 4851 = 7683984 = 2772^2 is a perfect square
2178 * 8712 = 18974736 = 4356^2 is a perfect square
4851 * 1584 = 7683984 = 2772^2 is a perfect square
8712 * 2178 = 18974736 = 4356^2 is a perfect square
10989 * 98901 = 1086823089 = 32967^2 is a perfect square
13104 * 40131 = 525876624 = 22932^2 is a perfect square
14544 * 44541 = 647804304 = 25452^2 is a perfect square
15984 * 48951 = 782432784 = 27972^2 is a perfect square
20808 * 80802 = 1681328016 = 41004^2 is a perfect square
21978 * 87912 = 1932129936 = 43956^2 is a perfect square
26208 * 80262 = 2103506496 = 45864^2 is a perfect square
27648 * 84672 = 2341011456 = 48384^2 is a perfect square
27848 * 84872 = 2363515456 = 48616^2 is a perfect square
36828 * 82863 = 3051678564 = 55242^2 is a perfect square
40131 * 13104 = 525876624 = 22932^2 is a perfect square
44541 * 14544 = 647804304 = 25452^2 is a perfect square
48139 * 93184 = 4485784576 = 66976^2 is a perfect square
48951 * 15984 = 782432784 = 27972^2 is a perfect square
49686 * 68694 = 3413130084 = 58422^2 is a perfect square
57399 * 99375 = 5704025625 = 75525^2 is a perfect square
68694 * 49686 = 3413130084 = 58422^2 is a perfect square
80262 * 26208 = 2103506496 = 45864^2 is a perfect square
80802 * 20808 = 1681328016 = 41004^2 is a perfect square
82863 * 36828 = 3051678564 = 55242^2 is a perfect square
84672 * 27648 = 2341011456 = 48384^2 is a perfect square
84872 * 27848 = 2363515456 = 48616^2 is a perfect square
87912 * 21978 = 1932129936 = 43956^2 is a perfect square
93184 * 48139 = 4485784576 = 66976^2 is a perfect square
98901 * 10989 = 1086823089 = 32967^2 is a perfect square
99375 * 57399 = 5704025625 = 75525^2 is a perfect square

]]> Comment on Integers such that √a + √b = √x by David a/k/a @InfinitelyManic http://benvitalenum3ers.wordpress.com/2013/05/19/integers-such-that-%e2%88%9aa-%e2%88%9ab-%e2%88%9ax/#comment-8977 Mon, 20 May 2013 03:03:09 +0000 http://benvitalenum3ers.wordpress.com/?p=11663#comment-8977 #!/usr/bin/python3
# David
# integers such that the sqrt(a) + sqrt(b) = sqrt(x)
from decimal import *
getcontext().prec=10
M=3
def getData():
abx = ((a,b,x) for a in range(2,10**M) for b in range(2,10**M) for x in range(2,10**M))
for t in abx:
yield t

get = getData()
while True:
try:
abx = next(get)
if Decimal(abx[0]).sqrt()+Decimal(abx[1]).sqrt() == Decimal(abx[2]).sqrt():
print(abx,Decimal(abx[0]).sqrt(),Decimal(abx[1]).sqrt(),Decimal(abx[0]).sqrt()+Decimal(abx[1]).sqrt(),De
cimal(abx[2]).sqrt())
except StopIteration:
break

#### some solutions
(2, 98, 128) 1.414213562 9.899494937 11.31370850 11.31370850
(2, 128, 162) 1.414213562 11.31370850 12.72792206 12.72792206
(2, 162, 200) 1.414213562 12.72792206 14.14213562 14.14213562
(2, 242, 288) 1.414213562 15.55634919 16.97056275 16.97056275
(2, 288, 338) 1.414213562 16.97056275 18.38477631 18.38477631
(2, 338, 392) 1.414213562 18.38477631 19.79898987 19.79898987
(2, 450, 512) 1.414213562 21.21320344 22.62741700 22.62741700
(2, 512, 578) 1.414213562 22.62741700 24.04163056 24.04163056
(2, 578, 648) 1.414213562 24.04163056 25.45584412 25.45584412
(2, 722, 800) 1.414213562 26.87005769 28.28427125 28.28427125
(2, 800, 882) 1.414213562 28.28427125 29.69848481 29.69848481
(2, 882, 968) 1.414213562 29.69848481 31.11269837 31.11269837
(3, 12, 27) 1.732050808 3.464101615 5.196152423 5.196152423
(3, 48, 75) 1.732050808 6.928203230 8.660254038 8.660254038
(3, 75, 108) 1.732050808 8.660254038 10.39230485 10.39230485
(3, 147, 192) 1.732050808 12.12435565 13.85640646 13.85640646
(3, 192, 243) 1.732050808 13.85640646 15.58845727 15.58845727
(3, 243, 300) 1.732050808 15.58845727 17.32050808 17.32050808
(3, 363, 432) 1.732050808 19.05255888 20.78460969 20.78460969
(3, 432, 507) 1.732050808 20.78460969 22.51666050 22.51666050

]]> Comment on Integers such that √a + √b = √x by themusegarden http://benvitalenum3ers.wordpress.com/2013/05/19/integers-such-that-%e2%88%9aa-%e2%88%9ab-%e2%88%9ax/#comment-8975 Sun, 19 May 2013 21:18:52 +0000 http://benvitalenum3ers.wordpress.com/?p=11663#comment-8975 small typo: the code is actually here: http://pastebin.com/NpXU2bky

]]> Comment on Integers such that √a + √b = √x by themusegarden http://benvitalenum3ers.wordpress.com/2013/05/19/integers-such-that-%e2%88%9aa-%e2%88%9ab-%e2%88%9ax/#comment-8974 Sun, 19 May 2013 21:17:17 +0000 http://benvitalenum3ers.wordpress.com/?p=11663#comment-8974 Not sure if this is all of them but I think so (forgive the kludgy code)
:
code: http://pastebin.com/FRpUGCji

output: http://pastebin.com/8dSi5fY7

465 solutions.

I chose only to use 1-31 in my loops because 31^2 = 961 and that’s the closest perfect square to 1000. What do you think?

]]> Comment on Integers such that √a + √b = √x by benvitalis http://benvitalenum3ers.wordpress.com/2013/05/19/integers-such-that-%e2%88%9aa-%e2%88%9ab-%e2%88%9ax/#comment-8973 Sun, 19 May 2013 20:14:41 +0000 http://benvitalenum3ers.wordpress.com/?p=11663#comment-8973 Right. the product a*b must be square

]]> Comment on Integers such that √a + √b = √x by Pat Ballew http://benvitalenum3ers.wordpress.com/2013/05/19/integers-such-that-%e2%88%9aa-%e2%88%9ab-%e2%88%9ax/#comment-8972 Sun, 19 May 2013 20:08:16 +0000 http://benvitalenum3ers.wordpress.com/?p=11663#comment-8972 I’m Picking 1,4 9 and let other people do the hard ones…. Seems as long as sqrt(ab) is integer, we should be able to find a,b,x that work.

]]> Comment on Concatenation of a num3er with itself by David @InfinitelyManic http://benvitalenum3ers.wordpress.com/2013/05/13/concatenation-of-a-num3er-with-itself/#comment-8949 Tue, 14 May 2013 16:27:40 +0000 http://benvitalenum3ers.wordpress.com/?p=11403#comment-8949 ### Some results for “Find numbers n such that n times n+6, n+7, n+8, n+9 … ”

n:95 n+6=101 n(n+6)=9595 or 95|95
n:3425 n+6=3431 n(n+6)=11751175 or 1175|1175
n:6570 n+6=6576 n(n+6)=43204320 or 4320|4320
n:9995 n+6=10001 n(n+6)=99959995 or 9995|9995
n:980199 n+6=980205 n(n+6)=960795960795 or 960795|960795
n:999995 n+6=1000001 n(n+6)=999995999995 or 999995|999995
n:41176465 n+6=41176471 n(n+6)=1695501516955015 or 16955015|16955015
n:58823530 n+6=58823536 n(n+6)=3460208034602080 or 34602080|34602080
n:99999995 n+6=100000001 n(n+6)=9999999599999995 or 99999995|99999995

n:94 n+7=101 n(n+7)=9494 or 94|94
n:7665 n+7=7672 n(n+7)=58805880 or 5880|5880
n:9994 n+7=10001 n(n+7)=99949994 or 9994|9994
n:356429 n+7=356436 n(n+7)=127044127044 or 127044|127044
n:643565 n+7=643572 n(n+7)=414180414180 or 414180|414180
n:999994 n+7=1000001 n(n+7)=999994999994 or 999994|999994
n:35294118 n+7=35294125 n(n+7)=1245675012456750 or 12456750|12456750
n:64705876 n+7=64705883 n(n+7)=4186850841868508 or 41868508|41868508
n:99999994 n+7=100000001 n(n+7)=9999999499999994 or 99999994|99999994

n:93 n+8=101 n(n+8)=9393 or 93|93
n:8760 n+8=8768 n(n+8)=76807680 or 7680|7680
n:9993 n+8=10001 n(n+8)=99939993 or 9993|9993
n:693062 n+8=693070 n(n+8)=480340480340 or 480340|480340
n:999993 n+8=1000001 n(n+8)=999993999993 or 999993|999993
n:88235287 n+8=88235295 n(n+8)=7785466577854665 or 77854665|77854665
n:99999993 n+8=100000001 n(n+8)=9999999399999993 or 99999993|99999993

n:92 n+9=101 n(n+9)=9292 or 92|92
n:9855 n+9=9864 n(n+9)=97209720 or 9720|9720
n:9992 n+9=10001 n(n+9)=99929992 or 9992|9992
n:970298 n+9=970307 n(n+9)=941486941486 or 941486|941486
n:999992 n+9=1000001 n(n+9)=999992999992 or 999992|999992
n:88235295 n+9=88235304 n(n+9)=7785468077854680 or 77854680|77854680
n:99999992 n+9=100000001 n(n+9)=9999999299999992 or 99999992|99999992

]]> Comment on Concatenation | N = M || M by benvitalis http://benvitalenum3ers.wordpress.com/2013/05/12/concatenation-n-m-m/#comment-8943 Mon, 13 May 2013 15:27:18 +0000 http://benvitalenum3ers.wordpress.com/?p=11451#comment-8943 Cool!

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