

A292201


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


1



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
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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)^c2 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^c2), c++); c; }


CROSSREFS

Subsequence of A255707.
Sequence in context: A165509 A100996 A232504 * A343070 A090048 A064285
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



