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

1,1

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

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.

Example

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

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 *)

Prog

(Magma) [ p: p in PrimesUpTo(770) | IsPrime(3*p-2) ]; // Klaus Brockhaus, Dec 21 2008
(PARI) list(lim)=select(p->isprime(3*p-2), primes(primepi(lim))) \\ Charles R Greathouse IV, Jul 25 2011
(Haskell)
a088878 n = a088878_list !! (n-1)
a088878_list = filter ((== 1) . a010051' . subtract 2 . (* 3)) a000040_list
-- Reinhard Zumkeller, Jul 02 2015

Crossrefs

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

Cf. A010051, A063908, A172287.

Cf. A259730.

Sequence in context: A350401 A154319 A080114 * A259730 A254673 A343976

Adjacent sequences: A088875 A088876 A088877 * A088879 A088880 A088881

Keyword

easy,nonn

Author

Giovanni Teofilatto, Nov 27 2003

Extensions

Corrected and extended by Ray Chandler, Dec 27 2003

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

Status

approved