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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.
1
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
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
KEYWORD
base,nonn
AUTHOR
Zak Seidov, Feb 10 2010
STATUS
approved