A173132 Numbers n with the property that both the sum of the even digits of n^2 and the sum of the odd digits of n^2 are squares.

0, 1, 2, 3, 7, 10, 20, 22, 30, 47, 67, 68, 70, 100, 115, 157, 158, 200, 202, 212, 220, 257, 283, 300, 392, 409, 470, 562, 599, 653, 670, 680, 700, 788, 832, 904, 1000, 1015, 1112, 1129, 1150, 1175, 1238, 1247, 1282, 1355, 1436, 1444, 1498, 1501, 1570, 1580, 1692

Offset

1,3

Comments

If n is in the sequence, then so is 10*n. - Robert Israel, Dec 27 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

67^2=4489, 4+4+8=16=4^2, 9=3^2; 115^2=13225, 2+2=4=2^2, 1+3+5=9=3^2.

Maple

filter:= proc(n) local L, E, O;
  L:= convert(n^2, base, 10);
  E, O:= selectremove(type, L, even);
  issqr(convert(E, `+`)) and issqr(convert(O, `+`))
end proc:
select(filter, [$0..2000]); # Robert Israel, Dec 27 2018

Prog

(PARI) isok(n) = {d = digits(n^2); sed = sum(i=1, #d, !(d[i]%2)*d[i]); sod = sum(i=1, #d, (d[i]%2)*d[i]); issquare(sed) && issquare(sod); } \\ Michel Marcus, Oct 15 2013

Crossrefs

Sequence in context: A271713 A355726 A356364 * A351704 A320675 A336414

Adjacent sequences: A173129 A173130 A173131 * A173133 A173134 A173135

Keyword

base,nonn

Author

Zak Seidov, Feb 10 2010

Status

approved