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

1,1

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

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.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Subsequence of A007528 and hence A016969.

Cf. A000040, A089253, A145471.

Sequence in context: A144918 A144920 A051615 * A181575 A335070 A354748

Adjacent sequences: A063906 A063907 A063908 * A063910 A063911 A063912

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Aug 31 2001

Status

approved