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

2,1

Links

Table of n, a(n) for n=2..24.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A056157 A142919 A142949 * A008993 A142088 A330810

Adjacent sequences: A061661 A061662 A061663 * A061665 A061666 A061667

Keyword

base,more,nonn

Author

Erich Friedman, Jun 16 2001

Extensions

More terms from Naohiro Nomoto, Oct 06 2001

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

Status

approved