A096599 Squares k^2 with property that A062892(k^2) = 1.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 225, 289, 324, 361, 484, 529, 576, 676, 729, 784, 841, 1156, 1225, 1444, 1521, 1681, 1849, 2116, 2209, 2601, 2704, 3025, 3136, 3249, 3364, 3481, 3721, 3844, 3969, 4225, 4356, 4489, 4624, 5041, 5184, 5329, 5476

Offset: 1

Author

Reinhard Zumkeller, Jun 29 2004

Keywords

• nonn
• base

Links

• David A. Corneth, Table of n, a(n) for n = 1..6883

Crossrefs

Cf. A096598, A096600, A000290, A000037, A039986.

Programs

Python

from math import isqrt
from sympy.utilities.iterables import multiset_permutations as mp
def sqr(n): return isqrt(n)**2 == n
def ok(square):
    s = str(square)
    perms = (int("".join(p)) for p in mp(s, len(s)))
    return len(set(p for p in perms if sqr(p))) == 1
def aupto(limit): return [k*k for k in range(isqrt(limit)+1) if ok(k*k)]
print(aupto(5476)) # Michael S. Branicky, Oct 18 2021

Extensions

Definition clarified by N. J. A. Sloane, Jan 16 2014