OFFSET
2,1
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
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