cp's OEIS Frontend

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

%I A362830 #26 Aug 02 2023 09:18:55
%S A362830 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,
%T A362830 17,20,19,21,22,23,21,25,26,27,25,29,27,30,30,30,32,34,31,35,34,37,37,
%U A362830 40,37,40,39,41,43,45,40,46,46,46,46,49,48,52,51,54,51
%N A362830 Number of bases b with 2 <= b < n such that n written in base b is a strictly increasing sequence of digits.
%H A362830 Michael S. Branicky, <a href="/A362830/b362830.txt">Table of n, a(n) for n = 1..10000</a>
%e A362830 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.
%t A362830 a[n_] := Count[Range[2, n], _?(Less @@ IntegerDigits[n, #] &)]; Array[a, 100] (* _Amiram Eldar_, Aug 02 2023 *)
%o A362830 (Python)
%o A362830 from sympy.ntheory import digits
%o A362830 def c(v): return all(v[i+1] > v[i] for i in range(len(v)-1))
%o A362830 def a(n): return sum(1 for b in range(2, n) if c(digits(n, b)[1:]))
%o A362830 print([a(n) for n in range(1, 71)]) # _Michael S. Branicky_, May 05 2023
%o A362830 (PARI) a(n) = sum(b=2, n-1, my(d=digits(n,b)); d==Set(d)); \\ _Michel Marcus_, May 07 2023
%K A362830 nonn,base
%O A362830 1,7
%A A362830 _Matthew R. Maas_, May 04 2023
%E A362830 a(33) and beyond from _Michael S. Branicky_, May 05 2023