A || B = A^2 + B^2

Numbers that are equal to the sum of the squares of their two “halves”

1233 = 12^2 + 33^2

8833 = 88^2 + 33^2

10,100 = 10^2 + 100^2

5,882,353 = 588^2 + 2353^2

 
Claudio Meller found http://oeis.org/A178530
 
990^2 + 100^2 = 990,100
9412^2 + 2353^2 = 94122353
17650^2 + 38125^2 = 1765038125
25840^2 + 43776^2 = 2584043776
74160^2 + 43776^2 = 7416043776
82350^2 + 38125^2 = 8235038125
 
 
 
DavidR noted:

Just enter the following in Wolfram Alpha to find more such numbers (changing 10000 to any other magnitude of 10 (Such as 10, 100, 1000, etc.):
integer solutions for 10000*a + b = a^2 + b^2, a > 0, b > 0

For example: 9412^2 + 2353^2 = 94,122,353
 
 
 
10000^2 + 1^2 = 100000001
 
 
1000*a + b = a^2 + b^2   gives
 
a = 0,   b = 0
a = 0,   b = 1
a = 10,   b = 100
a = 990,   b = 100
a = 1000,   b = 0
a = 1000,   b = 1
 
If for example,   4000*a + b = a^2 + b^2
 
a = 0,   b = 0
a = 0,   b = 1
a = 70,   b = 525
a = 100,   b = 625
a = 330,   b = 1101
a = 3670,   b = 1101
a = 3900,   b = 625
a = 3930,   b = 525
a = 4000,   b = 0
a = 4000,   b = 1
 
 
 

About these ads