A076164 Numbers k such that sum of squares of even digits of k equals sum of squares of odd digits.

0, 11112, 11121, 11211, 11356, 11365, 11536, 11563, 11635, 11653, 12111, 13156, 13165, 13516, 13561, 13615, 13651, 15136, 15163, 15316, 15361, 15613, 15631, 16135, 16153, 16315, 16351, 16513, 16531, 21111, 31156, 31165, 31516, 31561

Offset

1,2

Comments

The minimal number of digits in any nonzero term is 5.

Numbers such that the sum of even digits equals the sum of odd digits are listed in A036301.

Links

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

Example

11356 is in the sequence because 1^2 + 1^2 + 3^2 + 5^2 = 6^2.

Maple

filter:= proc(n) local t;
  add(t^2*(-1)^(t+1), t=convert(n, base, 10))=0
end proc:
select(filter, [$0..10^5]); # Robert Israel, Mar 17 2026

Mathematica

oeQ[n_]:=Module[{idn=IntegerDigits[n]}, Total[Select[idn, OddQ]^2]== Total[ Select[ idn, EvenQ]^2]]; Select[Range[0, 99999], oeQ] (* Harvey P. Dale, Sep 23 2011 *)

Prog

(PARI) is(n)=!vecsum(apply(d->d^2*(-1)^d, digits(n))) \\ M. F. Hasler, May 18 2018
(Python)
def ok(n):
    d, s = list(map(int, str(n))), [0, 0]
    for di in d: s[di&1] += di*di
    return s[0] == s[1]
print([k for k in range(32000) if ok(k)]) # Michael S. Branicky, Mar 17 2026

Crossrefs

Cf. A303269, A036301 (analog without squares), A071650, A304439, A304440, A124176, A124177.

Sequence in context: A262497 A291946 A154807 * A234661 A261778 A268278

Adjacent sequences: A076161 A076162 A076163 * A076165 A076166 A076167

Keyword

nonn,base

Author

Zak Seidov, Nov 01 2002

Extensions

Edited and a(1) = 0 added by M. F. Hasler, May 18 2018

Status

approved