cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A054037 #39 Oct 27 2023 22:00:46
%S A054037 10124,10128,10136,10214,10278,11826,12363,12543,12582,12586,13147,
%T A054037 13268,13278,13343,13434,13545,13698,14098,14442,14676,14743,14766,
%U A054037 15353,15681,15963,16549,16854,17252,17529,17778,17816,18072,19023,19377,19569,19629,20089
%N A054037 Numbers k such that k^2 contains exactly 9 different digits.
%C A054037 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
%H A054037 Sean A. Irvine, <a href="/A054037/b054037.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..83 from Zak Seidov)
%p A054037 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;
%t A054037 okQ[n_] := Module[{n2=n^2}, Max[DigitCount[n2,10]]==1 && IntegerLength[n2]==9]; Select[Range[20000], okQ]  (* _Harvey P. Dale_, Mar 20 2011 *)
%o A054037 (Python)
%o A054037 from itertools import count, islice
%o A054037 def agen(): yield from (k for k in count(10**4) if len(set(str(k*k)))==9)
%o A054037 print(list(islice(agen(), 37))) # _Michael S. Branicky_, May 24 2022
%Y A054037 Cf. A016069, A054031, A054032, A054033, A054034, A054035, A054036, A054038, A054039, A156977.
%K A054037 nonn,base
%O A054037 1,1
%A A054037 _Asher Auel_, Feb 28 2000