A045540 Numbers whose square contains an equal number of each digit that it contains.

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 16, 17, 18, 19, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 42, 43, 44, 48, 49, 51, 52, 53, 54, 55, 57, 59, 61, 64, 66, 69, 71, 72, 73, 74, 78, 79, 82, 84, 86, 87, 88, 89, 93, 95, 96, 98, 99, 113, 116, 117, 118, 124, 126, 128, 133, 134, 136

Offset

1,2

Comments

The sequence is expected to be infinite. Heuristically, if m is divisible by 10 there should be approximately constant * 10^(m/2)/m^(9/2) m-digit squares where all 10 digits have frequency m/10. - Robert Israel, Aug 14 2015

Links

Robert Israel, Table of n, a(n) for n = 1..3000

P. De Geest, Numbers whose digits occur with same frequency

Maple

filter:= proc(n) local x, i, P;
P:= add(x^i, i=convert(n^2, base, 10));
nops({coeffs(P, x)}) = 1
end proc:
select(filter, [$1..10^4]); # Robert Israel, Aug 14 2015

Mathematica

t={}; Do[If[Length[DeleteDuplicates[Transpose[Tally[IntegerDigits[n^2]]][[2]]]]==1, AppendTo[t, n]], {n, 136}]; t (* Jayanta Basu, May 10 2013 *)

Crossrefs

Cf. A052046, A052047, A052048, A052049, A052050, A052051, A052052, A052060.

Sequence in context: A213882 A135140 A052061 * A119509 A219248 A055568

Adjacent sequences: A045537 A045538 A045539 * A045541 A045542 A045543

Keyword

base,nonn,changed

Author

Erich Friedman

Status

approved