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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..70.

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

EXAMPLE

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.

MATHEMATICA

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

PROG

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

CROSSREFS

Subsequence of A255707.

Sequence in context: A165509 A100996 A232504 * A090048 A064285 A006694

Adjacent sequences:  A292198 A292199 A292200 * A292202 A292203 A292204

KEYWORD

nonn

AUTHOR

Michel Marcus, Sep 11 2017

EXTENSIONS

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

STATUS

approved

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Last modified September 22 16:56 EDT 2019. Contains 327311 sequences. (Running on oeis4.)