A237671 Let m_n denote the number which is obtained from n-base representation of m if its digits are written in nondecreasing order; then a(n) is the smallest period of the sequence which is defined by the recurrence b(0)=0, b(1)=1, b(k)=(b(k-1) + b(k-2))_n, for k>=2, or a(n)=0, if there is no such period.

1, 3, 16, 6, 20, 24, 16, 36, 120, 300, 20, 288, 28, 192, 200, 552, 180, 192, 180, 1380, 224, 60, 1728, 912, 3800, 756, 576, 1776, 4102, 15480, 3540, 1344, 10800, 14328, 800, 2304, 1520, 1890, 1232, 11280, 9040, 31152, 49544, 3660, 6360, 3696, 13248, 21408

Offset

2,2

Comments

We conjecture that the sequence b is always eventually periodic, and so a(n)>0.

Links

Pontus von Brömssen, Table of n, a(n) for n = 2..250 (terms 2..100 from Giovanni Resta)

Example

For n=5, b-sequence begins 0,1,1,2,3,1,4,1,1,2,... It has period {1,1,2,3,1,4} of length 6. So a(5)=6.
a(10) = 120, because the eventual period of A069638 is 120.

Prog

(Python)
import sympy, functools
def digits2int(x, b):
  return functools.reduce(lambda n, d:b*n+d, x, 0)
def A237671(n):
  return next(sympy.cycle_length(lambda x:(x[1], digits2int(sorted(sympy.ntheory.factor_.digits(sum(x), n)[1:]), n)), (0, 1)))[0] # Pontus von Brömssen, Aug 28 2020

Crossrefs

Cf. A069638, A237568, A004185, A306773.

Sequence in context: A054793 A063709 A195880 * A286199 A287080 A286966

Adjacent sequences: A237668 A237669 A237670 * A237672 A237673 A237674

Keyword

nonn,base

Author

Vladimir Shevelev and Peter J. C. Moses, Feb 11 2014

Status

approved