

A045540


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


11



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
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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) mdigit 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


AUTHOR

Erich Friedman


STATUS

approved



