OFFSET
1,3
COMMENTS
The sum of two numbers a1 and a2 that share a common b has the form of 10^n. Example: 12 + 88 = 100
The ordered pair of the final digit of a and b is always one of (0,0), (0,1), (0,5), (0,6), (2,3), (8,3), (2,8), or (8,8).
If b has k decimal digits, then (2a - 10^k)^2 + (2b - 1)^2 = 10^(2k) + 1 giving a way for efficient computation of many terms. - Max Alekseyev, Aug 17 2013
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..200
EXAMPLE
0 = 0^2+0^2 [this seems a bit far-fetched. - N. J. A. Sloane, Dec 23, 2010]
1=0^2+1^2 [ditto]
100=10^2+0^2.
101=10^2+1^2.
1233=12^2+33^2.
MATHEMATICA
Sort[Reap[Do[n=a^2+b^2; If[n==FromDigits[Join[IntegerDigits[a], IntegerDigits[b]]], Sow[n]], {a, 0, 1000}, {b, 0, 1000}]][[2, 1]]]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Karsten Meyer, Dec 23 2010
EXTENSIONS
Edited by N. J. A. Sloane, Dec 23 2010
a(11)-a(14) from Nathaniel Johnston, Jan 03 2011
Terms a(15) onward from Max Alekseyev, Aug 17 2013
STATUS
approved