A063909 Primes p such that 2*p - 5 is also prime.

5, 11, 17, 23, 29, 47, 53, 59, 71, 89, 101, 131, 137, 149, 179, 197, 227, 233, 257, 263, 281, 311, 353, 383, 389, 401, 431, 443, 467, 479, 491, 509, 557, 593, 599, 617, 641, 647, 653, 683, 719, 743, 809, 821, 857, 863, 941, 947, 953, 977, 1109

Offset: 1

Author

N. J. A. Sloane, Aug 31 2001

Keywords

• nonn
• easy

Comments

All terms are == 5 (mod 6). - Zak Seidov, Jan 07 2014

There are several interesting computer generated conjectures for this sequence at Jon Maiga's Sequence Machine site. - Antti Karttunen, Dec 07 2021

Note that 5, p, 2p - 5 form an arithmetic progression (PAP-3). - Charles R Greathouse IV, Mar 03 2025

Examples

			29 is in the sequence since p = 29 is prime and 2*p - 5 = 53 is also prime.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25000 (first 1000 terms from Harry J. Smith)
• Jon Maiga, Computer-generated formulas for A063909, Sequence Machine.

Crossrefs

Subsequence of A007528 and hence A016969.

Cf. A000040, A089253, A145471.

Programs

Magma

[p: p in PrimesUpTo(2000) | IsPrime(2*p-5)]; // Vincenzo Librandi, Feb 25 2016

Mathematica

Select[Prime[Range[500]],PrimeQ[2#-5]&] (* Harvey P. Dale, Oct 10 2011 *)

PARI

{ n=0; p=1; for (m=1, 10^9, p=nextprime(p+1); if (isprime(2*p - 5), write("b063909.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 02 2009

PARI

isA063909(p) = ((p%2)&&isprime(p)&&isprime(p+p-5)); \\ Antti Karttunen, Dec 07 2021

PARI

list(lim)=my(v=List()); forprimestep(p=5,lim\1,6, if(isprime(2*p-5), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Mar 03 2025

Formula

Intersection of A089253 and A000040. - Michael B. Porter, Jan 07 2014

a(n) = (A145471(n)+5)/2. [Also listed by Sequence Machine, and obviously true] - Antti Karttunen, Dec 07 2021