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

10, 18, 40, 46, 52, 61, 63, 90, 94, 106, 108, 112, 136, 148, 160, 163, 180, 184, 205, 211, 234, 243, 250, 252, 259, 265, 279, 295, 297, 298, 306, 316, 342, 360, 406, 409, 414, 418, 423, 432, 448, 460, 478, 481, 487, 490, 502, 520, 522, 526, 562, 567, 592

Offset: 1

Author

R. Muller

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2500
• F. Smarandache, Only Problems, Not Solutions!, Xiquan Publ., Phoenix-Chicago, 1993.

Crossrefs

Cf. A000290, A062892, A096600.

Programs

Mathematica

Select[Range[600],!IntegerQ[Sqrt[#]]&&AnyTrue[FromDigits/@ Permutations[ IntegerDigits[ #]],IntegerQ[ Sqrt[#]]&]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 17 2020 *)

Python

from math import isqrt
from sympy.utilities.iterables import multiset_permutations as mp
def sqr(n): return isqrt(n)**2 == n
def ok(n):
    if sqr(n): return False
    s = str(n)
    return any(sqr(int("".join(p))) for p in mp(s, len(s)))
print([k for k in range(600) if ok(k)]) # Michael S. Branicky, Oct 18 2021

Formula

A062892(a(n)) > 0.

Extensions

More terms from Reinhard Zumkeller, Jun 29 2004