A344887 a(n) is the least base k >= 2 that the base-k digits of n are nonincreasing.

2, 2, 2, 2, 2, 4, 2, 2, 2, 3, 4, 5, 2, 3, 2, 2, 2, 5, 3, 6, 4, 3, 3, 5, 2, 3, 3, 3, 2, 7, 2, 2, 2, 6, 6, 6, 3, 4, 7, 3, 3, 4, 4, 6, 7, 7, 7, 7, 2, 7, 5, 8, 4, 4, 3, 5, 2, 4, 4, 8, 2, 4, 2, 2, 2, 9, 3, 3, 9, 9, 9, 10, 3, 8, 9, 3, 3, 9, 3, 3, 3, 3, 10, 10, 4, 4

Offset

0,1

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Formula

a(n) <= A000196(n) + 2.

a(n) <= 10 for any n in A009996.

a(n) = 2 iff n belongs to A023758.

Example

For n = 258:
- we have:
     b  258 in base b  Nonincreasing?
     -  -------------  --------------
     2      100000010  No
     3         100120  No
     4          10002  No
     5           2013  No
     6           1110  Yes
- so a(258) = 6.

Mathematica

Table[k=1; While[AnyTrue[Differences@IntegerDigits[n, ++k], #>0&]]; k, {n, 0, 100}] (* Giorgos Kalogeropoulos, Jun 02 2021 *)

Prog

(PARI) a(n) = { for (b=2, oo, my (d=digits(n, b)); if (d==vecsort(d, , 4), return (b))) }
(Python) # with library / without (faster for large n)
from sympy.ntheory import digits
def is_nondec(n, b): d = digits(n, b)[1:]; return d == sorted(d)[::-1]
def is_nondec(n, b):
  if n < b: return True
  n, r = divmod(n, b)
  while n >= b:
    (n, r), lastd = divmod(n, b), r
    if r < lastd: return False
  return n >= r
def a(n):
  for b in range(2, n+3):
    if is_nondec(n, b): return b
print([a(n) for n in range(86)]) # Michael S. Branicky, Jun 01 2021

Crossrefs

Cf. A000196, A009996, A023758, A273040.

Sequence in context: A239202 A083533 A076500 * A060594 A327813 A104361

Adjacent sequences: A344884 A344885 A344886 * A344888 A344889 A344890

Keyword

nonn,base

Author

Rémy Sigrist, Jun 01 2021

Status

approved