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
Examples
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.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
Programs
-
Mathematica
Table[k=1;While[AnyTrue[Differences@IntegerDigits[n,++k],#>0&]];k,{n,0,100}] (* Giorgos Kalogeropoulos, Jun 02 2021 *) -
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