login
A364089
a(n) is the greatest k such that the base-n digits of 2^k are all distinct.
2
1, 1, 3, 4, 5, 8, 5, 10, 29, 19, 19, 19, 16, 18, 7, 43, 41, 37, 45, 39, 55, 33, 43, 60, 35, 61, 56, 50, 44, 69, 9, 64, 44, 80, 43, 88, 53, 71, 56, 68, 59, 78, 76, 74, 95, 109, 111, 81, 86, 136, 117, 75, 98, 83, 84, 99, 104, 116, 95, 118, 60, 81, 11, 119, 119, 172, 140, 97, 105, 113, 93, 122, 92
OFFSET
2,3
COMMENTS
a(n) <= log_2(A062813(n)).
EXAMPLE
a(10) = 29 because all decimal digits of 2^29 = 536870912 are distinct.
MAPLE
f:= proc(b) local M, k, L;
M:= b^b - (b^b-b)/(b-1)^2;
for k from ilog2(M) to 1 by -1 do
L:= convert(2^k, base, b);
if nops(L) = nops(convert(L, set)) then return k fi
od
end proc:
map(f, [$2..100]);
PROG
(Python)
from sympy.ntheory.factor_ import digits
def A364089(n):
m = 1<<(l:=((r:=n**n)-(r-n)//(n-1)**2).bit_length()-1)
while len(d:=digits(m, n)[1:]) > len(set(d)):
l -= 1
m >>= 1
return l # Chai Wah Wu, Jul 07 2023
KEYWORD
nonn,base
AUTHOR
Robert Israel, Jul 04 2023
STATUS
approved