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A045540
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Numbers whose square contains an equal number of each digit that it contains.
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11
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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
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1,2
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COMMENTS
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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
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..3000
P. De Geest, Numbers whose digits occur with same frequency
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MAPLE
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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
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MATHEMATICA
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t={}; Do[If[Length[DeleteDuplicates[Transpose[Tally[IntegerDigits[n^2]]][[2]]]]==1, AppendTo[t, n]], {n, 136}]; t (* Jayanta Basu, May 10 2013 *)
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CROSSREFS
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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
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KEYWORD
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base,nonn
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AUTHOR
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Erich Friedman
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STATUS
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approved
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