A292201 a(n) is the smallest value c such that prime(n)^c - 2 is prime, where prime(n) is the n-th prime or -1 if no such c exists.

2, 2, 1, 1, 4, 1, 6, 1, 24, 2, 1, 2, 4, 1, 2, 4, 4, 1, 3, 2, 1, 38, 4, 2, 747, 4, 1, 2, 1, 10, 2, 2, 10, 1, 50, 1, 22, 38, 12, 2, 40, 1, 2, 1, 164, 1, 2, 2, 12, 1, 2, 2, 1, 8, 2, 18, 22, 1, 3, 10, 1, 2, 102, 4, 1, 13896, 12, 2, 1122, 1

Offset: 1

Author

Michel Marcus, Sep 11 2017

Keywords

• nonn

Comments

a(71) > 38000 (if it exists). - Robert Price, Oct 23 2017

Examples

			a(1) = 2 because 2^2 - 2 = 2 is prime;
a(2) = 2 because 3^2 - 2 = 7 is prime;
a(3) = 1 because 5^1 - 2 = 3 is prime;
a(4) = 1 because 7^1 - 2 = 5 is prime.
And these are the least exponents to satisfy the requested property.
		

Links

• Carlos Rivera, Puzzle 887. p(n)^c-2 is prime, The Prime Puzzles and Problems Connection.

Crossrefs

Subsequence of A255707.

Programs

Mathematica

Table[c = 1; While[! PrimeQ[Prime[n]^c - 2], c++]; c, {n, 24}] (* Michael De Vlieger, Sep 11 2017 *)

PARI

a(n) = {my(c = 1, p = prime(n)); while(!isprime(p^c-2), c++); c;}

Extensions

a(66)-a(70) from Robert Price, Oct 23 2017