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A117588 Numbers k such that 2^k + prime(k)^2 is prime. 0
2, 6, 8, 14, 20, 90, 102, 154, 228, 310, 418, 554, 1070, 1224, 3144, 3996, 4464, 16194, 17096 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms are even since 2^k + prime(k)^2 == 0 (mod 3) for any odd number k. - Robert G. Wilson v Apr 03 2006

If k is odd, prime(k) == +- 1 (mod 3) making prime(k)^2 == 1 (mod 3) and 2^k == - 1 (mod 3). - Robert G. Wilson v Apr 03 2006

No more terms below 30000.

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

20 is in the sequence because the 20th prime is 71 and 2^20 + 71^2 = 1053617 is prime.

MAPLE

a:=proc(n) if isprime(2^n+ithprime(n)^2) then n else fi end: seq(a(n), n=1..1300); # Emeric Deutsch, Apr 06 2006

MATHEMATICA

Do[ If[ PrimeQ[2^n + Prime[n]^2], Print[n]], {n, 20000}] (* Robert G. Wilson v *)

PROG

(PARI) for(i=1, 3000, if(isprime(2^i+prime(i)^2), print1(i, ", ")))

CROSSREFS

Sequence in context: A212014 A270050 A137831 * A174229 A187217 A022112

Adjacent sequences:  A117585 A117586 A117587 * A117589 A117590 A117591

KEYWORD

nonn,more

AUTHOR

Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 03 2006

EXTENSIONS

a(15)-a(19) from Robert G. Wilson v and Giovanni Resta, Apr 03 2006

STATUS

approved

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Last modified November 13 15:41 EST 2019. Contains 329106 sequences. (Running on oeis4.)