A364052 a(n) is the least k such that no number with distinct base-n digits is the product of k (not necessarily distinct) primes.

2, 3, 7, 9, 12, 14, 14, 21, 26, 28, 33, 36, 40, 45, 36, 50, 59, 61, 65, 70, 75, 77, 85, 89, 94, 97, 104, 107, 113, 118, 84

Offset

2,1

Comments

A364049(n) <= a(n) <= 1 + floor(log_2(A062813(n))).

Links

Table of n, a(n) for n=2..32.

Example

a(4) = 7 because 2 = 2^1 = 2_4, 4 = 2^2 = 10_4, 8 = 2^3 = 20_4, 24 = 2^3 * 3 = 120_4, 108 = 2^2 * 3^3 = 1230_4 and 216 = 2^3 * 3^3 = 3120_4 have distinct base-4 digits and are products of 1 to 6 primes respectively, but there is no product of 7 primes that has distinct base-4 digits.

Maple

f:= proc(n) local d, S, V, k;
  V:= {};
  for d from 1 to n do
    S:= select(t -> t[-1] <> 0, combinat:-permute([$0..n-1], d));
    S:= map(proc(t) local i;  numtheory:-bigomega(add(t[i]*n^(i-1), i=1..d)) end proc, S);
    V:= V union convert(S, set);
  od;
  min({$1..1+max(V)} minus V)
end proc:
map(f, [$2..10]);

Crossrefs

Cf. A001222, A062813, A165712, A364049.

Sequence in context: A328982 A260641 A077510 * A178433 A073148 A014839

Adjacent sequences: A364049 A364050 A364051 * A364053 A364054 A364055

Keyword

nonn,base,hard,more

Author

Robert Israel, Jul 04 2023

Extensions

a(11) from Jon E. Schoenfield, Jul 05 2023

a(12) from Martin Ehrenstein, Jul 07 2023

a(13)-a(18) from Jon E. Schoenfield, Jul 08 2023

a(19)-a(22) from Pontus von Brömssen, Jul 13 2023

a(23)-a(32) from Bert Dobbelaere, Jul 20 2023

Status

approved