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 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 (list; graph; refs; listen; history; text; internal format)
 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 AUTHOR STATUS approved

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Last modified June 29 14:08 EDT 2022. Contains 354913 sequences. (Running on oeis4.)