A061664 a(n) is the smallest number k >= 2 for which k and k^2 contain the same digits in the same proportion in base n.

53, 184, 45, 9726, 3697, 30, 266, 2890, 72576, 121892, 1604132, 22423892, 31215, 61572224, 532740, 49520, 495341325, 7900478246, 19972726643, 1006557500, 1163503182, 8736, 936946009

Offset: 2

Author

Erich Friedman, Jun 16 2001

Keywords

• base
• more
• nonn

Examples

			a(9) = 2890 since 2890 = 3861 in base 9 and 2890^2 = 16638831 in base 9.
		

Crossrefs

Cf. A061656, A061657, A061658, A061659, A061660, A061661, A061662, A061663, A114258.

Programs

Python

from fractions import Fraction
from sympy.ntheory import digits
from itertools import count, islice
def f(i, j, base):
    si, sj = digits(i, base)[1:], digits(j, base)[1:]
    pi = [Fraction(si.count(d), len(si)) for d in range(base)]
    pj = [Fraction(sj.count(d), len(sj)) for d in range(base)]
    return pi == pj
def a(n): return next(k for k in count(2) if f(k, k**2, n))
print([a(n) for n in range(2, 12)]) # Michael S. Branicky, Feb 27 2023

Extensions

More terms from Naohiro Nomoto, Oct 06 2001

Title clarified and a(15)-a(24) from Sean A. Irvine, Feb 27 2023