A358536 a(n) is the least prime factor of 2^n-n-2.

3, 2, 5, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 13, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 29, 2, 5, 2, 3, 2, 73, 2, 23, 2, 3, 2, 29, 2, 43, 2, 3, 2, 47, 2, 7, 2, 3, 2, 37, 2, 113, 2, 3, 2, 11, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 5, 2, 73, 2, 3, 2, 53, 2, 79, 2, 3, 2, 11, 2, 5, 2, 3, 2, 61, 2, 5, 2, 3, 2

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).

Formula

a(n) = A020639(A000247(n)).

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

Cf. A000247, A020639.

Sequence in context: A075410 A023513 A069735 * A274457 A328579 A046524

Adjacent sequences: A358533 A358534 A358535 * A358537 A358538 A358539

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 21 2022

Status

approved