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A227126 Primes p_i such that 2^(i+1) - p_i is also prime. 4
2, 3, 5, 11, 17, 167, 193, 197, 433, 4111, 9173, 42929, 95279, 98897, 139409, 142567, 228617, 329333, 344209, 791191, 829177 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The corresponding primes 2^(i + 1) - prime(i) are 2, 5, 11, 53, 239, 1099511627609, 35184372088639, ...

The prime indices i are 1, 2, 3, 5, 7, 39, 44, 45, 84, 566, 1137, ...

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

5 is a term because 5 is the 3rd prime, and 2^(3+1) - 5 = 16 - 5 = 11 which is a prime

11 is in the sequence because 11 = prime(5) and 2^(5 + 1) - 11 = 64 - 11 = 53 is a prime.

MATHEMATICA

p = 2; lst = {}; While[p < 850001, If[ PrimeQ[ 2^(PrimePi@ p +1) - p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst \\ Robert G. Wilson v, Jul 09 2014

PROG

(PARI) lista(nn) = {ip = 1; forprime(p=2, nn, if (isprime(2^(ip+1)-p), print1(p, ", ")); ip++; ); } \\ Michel Marcus, Jul 12 2014

CROSSREFS

Cf. A078686, A244913.

Sequence in context: A097048 A286268 A244914 * A057652 A025067 A024371

Adjacent sequences:  A227123 A227124 A227125 * A227127 A227128 A227129

KEYWORD

nonn,more

AUTHOR

Gerasimov Sergey, Jul 02 2013

EXTENSIONS

a(3), a(6), a(8)- a(12) from Joerg Arndt, Jul 03 2013

Corrected and extended through a(21) by Robert G. Wilson v, Jul 09 2014

Entry revised by N. J. A. Sloane, Jan 02 2019, incorporating data from a later submission from Robert G. Wilson v

STATUS

approved

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)