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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. 1

%I

%S 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,

%T 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,

%U 1,2,102,4,1,13896,12,2,1122,1

%N 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.

%C a(71) > 38000 (if it exists). - _Robert Price_, Oct 23 2017

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_887.htm">Puzzle 887. p(n)^c-2 is prime</a>, The Prime Puzzles and Problems Connection.

%e a(1) = 2 because 2^2 - 2 = 2 is prime;

%e a(2) = 2 because 3^2 - 2 = 7 is prime;

%e a(3) = 1 because 5^1 - 2 = 3 is prime;

%e a(4) = 1 because 7^1 - 2 = 5 is prime.

%e And these are the least exponents to satisfy the requested property.

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

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

%Y Subsequence of A255707.

%K nonn

%O 1,1

%A _Michel Marcus_, Sep 11 2017

%E a(66)-a(70) from _Robert Price_, Oct 23 2017

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Last modified August 2 20:05 EDT 2021. Contains 346428 sequences. (Running on oeis4.)