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
KEYWORD
nonn,base
AUTHOR
Matthew R. Maas, May 04 2023
EXTENSIONS
a(33) and beyond from Michael S. Branicky, May 05 2023
STATUS
approved