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Number of n-digit numbers x such that the digits of x^2 occur with frequency 1.
0

%I #5 Jun 21 2013 16:45:40

%S 10,49,162,220,170,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Number of n-digit numbers x such that the digits of x^2 occur with frequency 1.

%C After a(5), all terms are 0.

%e All numbers 0 to 9 have squares containing only digits of frequency 1: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81.

%t cnt = 0; x = 0; t2 = Table[While[x < 10^n, If[Union[Last[Transpose[Tally[IntegerDigits[x^2]]]]] == {1}, cnt++]; x++]; cnt, {n, 5}]; Differences[Join[{0}, t2]]

%Y Cf. A225428, A226796.

%K nonn,base

%O 1,1

%A _T. D. Noe_, Jun 21 2013

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