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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 (list; graph; refs; listen; history; text; internal format)
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: A213075 A100847 A271713 * A320675 A336414 A095010

Adjacent sequences:  A173129 A173130 A173131 * A173133 A173134 A173135

KEYWORD

base,nonn

AUTHOR

Zak Seidov, Feb 10 2010

STATUS

approved

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Last modified January 24 19:34 EST 2022. Contains 350565 sequences. (Running on oeis4.)