A362830 Number of bases b with 2 <= b < n such that n written in base b is a strictly increasing sequence of digits.

0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 5, 4, 6, 6, 7, 7, 9, 8, 11, 10, 11, 12, 14, 12, 15, 15, 17, 16, 19, 17, 20, 19, 21, 22, 23, 21, 25, 26, 27, 25, 29, 27, 30, 30, 30, 32, 34, 31, 35, 34, 37, 37, 40, 37, 40, 39, 41, 43, 45, 40, 46, 46, 46, 46, 49, 48, 52, 51, 54, 51

Offset

1,7

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

The number 27 forms a strictly increasing sequence of digits when written in base 4 (1,2,3), base 7 (3,6), base 10 (2,7), base 11 (2,5), base 12 (2,3), and bases 14 through 25 (1,13 through 1,2), and no other bases below 27. There are 17 bases with this property, so a(27)=17.

Mathematica

a[n_] := Count[Range[2, n], _?(Less @@ IntegerDigits[n, #] &)]; Array[a, 100] (* Amiram Eldar, Aug 02 2023 *)

Prog

(Python)
from sympy.ntheory import digits
def c(v): return all(v[i+1] > v[i] for i in range(len(v)-1))
def a(n): return sum(1 for b in range(2, n) if c(digits(n, b)[1:]))
print([a(n) for n in range(1, 71)]) # Michael S. Branicky, May 05 2023
(PARI) a(n) = sum(b=2, n-1, my(d=digits(n, b)); d==Set(d)); \\ Michel Marcus, May 07 2023

Crossrefs

Sequence in context: A323608 A122352 A338903 * A248519 A326670 A361178

Adjacent sequences: A362827 A362828 A362829 * A362831 A362832 A362833

Keyword

nonn,base

Author

Matthew R. Maas, May 04 2023

Extensions

a(33) and beyond from Michael S. Branicky, May 05 2023

Status

approved