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A317909
Primes p such that prime(p) + p + 1 is prime.
2
5, 11, 23, 29, 59, 97, 109, 137, 139, 149, 197, 257, 263, 269, 283, 293, 317, 347, 359, 421, 431, 569, 587, 593, 601, 617, 643, 647, 653, 677, 683, 691, 709, 761, 797, 809, 839, 881, 947, 977, 983, 1091, 1163, 1213, 1237, 1259, 1361, 1373
OFFSET
1,1
COMMENTS
It appears that the resulting primes are a subsequence of A112885. - Michel Marcus, Aug 16 2018
If p is a prime in this sequence, then prime(p)+p+1 is prime. Put k = p+1, then prime(p)+p+1 = prime(k-1)+k, and is prime, so is in A112885. Therefore the resulting primes of this sequence are a subsequence of A112885. - David James Sycamore, Aug 16 2018
LINKS
EXAMPLE
Prime(5)+5+1 = 11+5+1 = 17 therefore 5 is a member of the sequence, and is the first such prime, hence a(1) = 5.
MAPLE
N := 2000;
for X from 1 to N do
Z := ithprime(X);
P := Z+X+1;
if isprime(X) and isprime(P) then print(X);
end if
end do
MATHEMATICA
Select[Prime@ Range@ 300, PrimeQ[# + Prime[#] + 1] &] (* Giovanni Resta, Aug 16 2018 *)
PROG
(PARI) isok(p) = isprime(p) && isprime(prime(p) + p + 1); \\ Michel Marcus, Aug 16 2018
CROSSREFS
Cf. A112885.
Sequence in context: A152533 A228485 A161896 * A304372 A167610 A295149
KEYWORD
nonn
AUTHOR
STATUS
approved