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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

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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);