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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

%I #10 Dec 27 2018 22:03:36

%S 0,1,2,3,7,10,20,22,30,47,67,68,70,100,115,157,158,200,202,212,220,

%T 257,283,300,392,409,470,562,599,653,670,680,700,788,832,904,1000,

%U 1015,1112,1129,1150,1175,1238,1247,1282,1355,1436,1444,1498,1501,1570,1580,1692

%N 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.

%C If n is in the sequence, then so is 10*n. - _Robert Israel_, Dec 27 2018

%H Robert Israel, <a href="/A173132/b173132.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p filter:= proc(n) local L,E,O;

%p L:= convert(n^2,base,10);

%p E,O:= selectremove(type,L,even);

%p issqr(convert(E,`+`)) and issqr(convert(O,`+`))

%p end proc:

%p select(filter, [$0..2000]); # _Robert Israel_, Dec 27 2018

%o (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

%K base,nonn

%O 1,3

%A _Zak Seidov_, Feb 10 2010

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Last modified April 25 13:34 EDT 2024. Contains 371971 sequences. (Running on oeis4.)