OFFSET
3,1
COMMENTS
a(n) = 2 if n is even.
a(n) = 3 if n == 3 (mod 6).
a(n) = 5 if n == 5 or 11 (mod 20) and is not divisible by 3.
a(n) <= n if n is prime.
a(n) = A000247(n) for n = 3 and (subject to confirmation of probable primes) 39137 and 59819. The latter two were discovered by Henri Lifchitz in 2005.
LINKS
Robert Israel, Table of n, a(n) for n = 3..516
R. Israel and R. Fernando, Primes 2^n-n-2, Mathematics StackExchange (2022).
EXAMPLE
a(5) = 5 because 2^5 - 5 - 2 = 25 has least prime factor 5.
MAPLE
f:= proc(n) local F;
F:= select(type, map(t -> t[1], ifactors(2^n-n-2, easy)[2]), posint);
if F = [] then F:= map(t -> t[1], ifactors(2^n-n-2)[2])) fi;
min(F);
end proc:
map(f, [$3..100]);
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Nov 21 2022
STATUS
approved