

A321084


Primes prime(n) such that 1 + Sum_{k=1..n} 2^(prime(k)1) is prime.


0




OFFSET

1,1


COMMENTS

Primes prime(n) such that A080355(n+1) is prime.
The prime p = 19 gives the prime 332887 = 1010001010001010111_2.
The positions of 1's from the end are 1, 2, 3, 5, 7, 11, 13, 17, 19.
Let S(n) = Sum_{k=1..n} 2^(prime(k)1). Conjecture: q(n) = 1 + S(n) is prime if and only if 2^S(n) == 1 (mod q(n)).


LINKS



EXAMPLE

a(3) = 5 since 1 + 2^(21) + 2^(31) + 2^(51) = 10111_2 = 23 is prime.
Note that prime(3) = 5 and A080355(3+1) = 23 prime.


MATHEMATICA

Prime@ Select[Range[10^3], PrimeQ[1 + Total@ Array[2^(Prime[#]  1) &, #]] &] (* Michael De Vlieger, Oct 31 2018 *)


PROG

(PARI) isok(p) = isprime(p) && isprime(1 + sum(k=1, primepi(p), 2^(prime(k)1))); \\ Michel Marcus, Oct 27 2018


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



