A054037 Numbers k such that k^2 contains exactly 9 different digits.

10124, 10128, 10136, 10214, 10278, 11826, 12363, 12543, 12582, 12586, 13147, 13268, 13278, 13343, 13434, 13545, 13698, 14098, 14442, 14676, 14743, 14766, 15353, 15681, 15963, 16549, 16854, 17252, 17529, 17778, 17816, 18072, 19023, 19377, 19569, 19629, 20089

Offset

1,1

Comments

There are three prime numbers {13147, 20089, 21397} and corresponding squares {172843609, 403567921, 457831609} necessarily contain zero (otherwise n and n^2 are divisible by 3). - Zak Seidov, Jan 18 2012

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000 (terms 1..83 from Zak Seidov)

Maple

f := []; for i from 0 to 200 do if nops({op(convert(i^2, base, 10))})=9 then f := [op(f), i] fi; od; f;

Mathematica

okQ[n_] := Module[{n2=n^2}, Max[DigitCount[n2, 10]]==1 && IntegerLength[n2]==9]; Select[Range[20000], okQ]  (* Harvey P. Dale, Mar 20 2011 *)

Prog

(Python)
from itertools import count, islice
def agen(): yield from (k for k in count(10**4) if len(set(str(k*k)))==9)
print(list(islice(agen(), 37))) # Michael S. Branicky, May 24 2022

Crossrefs

Cf. A016069, A054031, A054032, A054033, A054034, A054035, A054036, A054038, A054039, A156977.

Sequence in context: A157711 A159863 A234180 * A289856 A023066 A248487

Adjacent sequences: A054034 A054035 A054036 * A054038 A054039 A054040

Keyword

nonn,base

Author

Asher Auel, Feb 28 2000

Status

approved