A088878 Prime numbers p such that 3p - 2 is a prime.

3, 5, 7, 11, 13, 23, 37, 43, 47, 53, 61, 67, 71, 103, 113, 127, 137, 163, 167, 181, 191, 193, 211, 251, 257, 263, 271, 277, 293, 307, 313, 331, 337, 347, 373, 401, 431, 433, 443, 461, 467, 487, 491, 523, 541, 557, 587, 593, 601, 673, 677, 727, 751, 757, 761

Offset: 1

Author

Giovanni Teofilatto, Nov 27 2003

Keywords

• easy
• nonn

Comments

Indices of semiprime octagonal numbers. - Jonathan Vos Post, Feb 16 2006

Daughter primes of order 1. - Artur Jasinski, Dec 12 2007

A010051(3*a(n)-2) = 1. - Reinhard Zumkeller, Jul 02 2015

Examples

			For p = 3, 3p - 2 = 7;
for p = 523, 3p - 2 = 1567.
		

References

• M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
• Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta, UTET, CittaStudiEdizioni, Milano 1997

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Octagonal Number.
• Eric Weisstein's World of Mathematics, Semiprime.

Crossrefs

Cf. A000040, A000567, A001222, A001358, A091179, A091180, A091181, A136019, A136020, A153183, A153184.

Cf. A010051, A063908, A172287.

Cf. A259730.

Programs

Haskell

a088878 n = a088878_list !! (n-1)
a088878_list = filter ((== 1) . a010051' . subtract 2 . (* 3)) a000040_list
-- Reinhard Zumkeller, Jul 02 2015

Magma

[ p: p in PrimesUpTo(770) | IsPrime(3*p-2) ]; // Klaus Brockhaus, Dec 21 2008

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[3*p-2],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 22 2008 *)
n = 1; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, (Prime[k] + 2n)/(2n + 1)]], {k, 1, 500}]; a (* Artur Jasinski, Dec 12 2007 *)
Select[Prime[Range[150]],PrimeQ[3#-2]&] (* Harvey P. Dale, Feb 27 2024 *)

PARI

list(lim)=select(p->isprime(3*p-2),primes(primepi(lim))) \\ Charles R Greathouse IV, Jul 25 2011

Extensions

Corrected and extended by Ray Chandler, Dec 27 2003

Entry revised by N. J. A. Sloane, Nov 28 2006, Jul 08 2010