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.

A007937 Nonsquares such that some permutation of digits is a square.

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%I A007937 #18 Oct 18 2021 11:19:41
%S A007937 10,18,40,46,52,61,63,90,94,106,108,112,136,148,160,163,180,184,205,
%T A007937 211,234,243,250,252,259,265,279,295,297,298,306,316,342,360,406,409,
%U A007937 414,418,423,432,448,460,478,481,487,490,502,520,522,526,562,567,592
%N A007937 Nonsquares such that some permutation of digits is a square.
%H A007937 Harvey P. Dale, <a href="/A007937/b007937.txt">Table of n, a(n) for n = 1..2500</a>
%H A007937 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>, Xiquan Publ., Phoenix-Chicago, 1993.
%F A007937 A062892(a(n)) > 0.
%t A007937 Select[Range[600],!IntegerQ[Sqrt[#]]&&AnyTrue[FromDigits/@ Permutations[ IntegerDigits[ #]],IntegerQ[ Sqrt[#]]&]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 17 2020 *)
%o A007937 (Python)
%o A007937 from math import isqrt
%o A007937 from sympy.utilities.iterables import multiset_permutations as mp
%o A007937 def sqr(n): return isqrt(n)**2 == n
%o A007937 def ok(n):
%o A007937     if sqr(n): return False
%o A007937     s = str(n)
%o A007937     return any(sqr(int("".join(p))) for p in mp(s, len(s)))
%o A007937 print([k for k in range(600) if ok(k)]) # _Michael S. Branicky_, Oct 18 2021
%Y A007937 Cf. A000290, A062892, A096600.
%K A007937 nonn,base
%O A007937 1,1
%A A007937 R. Muller
%E A007937 More terms from _Reinhard Zumkeller_, Jun 29 2004