

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



