A364049 a(n) is the least k such that the base-n digits of 2^k are not all distinct.

2, 2, 4, 5, 6, 3, 6, 11, 16, 14, 11, 12, 8, 4, 8, 15, 16, 12, 16, 18, 9, 17, 15, 14, 24, 13, 16, 15, 10, 5, 10, 19, 24, 14, 21, 15, 18, 15, 19, 17, 17, 28, 18, 12, 24, 23, 31, 24, 31, 20, 26, 44, 35, 33, 25, 18, 36, 14, 14, 18, 12, 6, 12, 23, 45, 37, 38, 24, 20, 35, 36, 26, 51, 31, 33, 47, 34, 34

Offset

2,1

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Example

a(10) = 16 because 2^16 = 65536 does not have all distinct digits in base 10, while 2^k does have all distinct digits for 1 <= k <= 15.

Maple

f:= proc(n) local k, L;
  for k from 2 do
    L:= convert(2^k, base, n);
    if nops(L) <> nops(convert(L, set)) then return k fi
  od;
end proc:
map(f, [$2..100]);

Prog

(Python)
from itertools import count
from sympy.ntheory import digits
def a(n): return next(k for k in count(2) if len(set(d:=digits(1<<k, n)[1:]))<len(d))
print([a(n) for n in range(2, 80)]) # Michael S. Branicky, Jul 05 2023

Crossrefs

Cf. A004642, A004643, A000866, A004645, A004646, A004647, A001357, A000079, A011557, A364052, A364089.

Sequence in context: A085085 A121600 A126870 * A368866 A137413 A010848

Adjacent sequences: A364046 A364047 A364048 * A364050 A364051 A364052

Keyword

nonn,base

Author

Robert Israel, Jul 03 2023

Status

approved