cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Giovanni Teofilatto, Nov 27 2003

Keywords

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

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

A091180 Primes of the form 3*p - 2 such that p is a prime.

Original entry on oeis.org

7, 13, 19, 31, 37, 67, 109, 127, 139, 157, 181, 199, 211, 307, 337, 379, 409, 487, 499, 541, 571, 577, 631, 751, 769, 787, 811, 829, 877, 919, 937, 991, 1009, 1039, 1117, 1201, 1291, 1297, 1327, 1381, 1399, 1459, 1471, 1567, 1621, 1669, 1759, 1777, 1801
Offset: 1

Views

Author

Ray Chandler, Dec 27 2003

Keywords

Comments

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

Examples

			From _K. D. Bajpai_, Jun 20 2015: (Start)
a(4) = 31: 3*11 - 2 = 31; A088878(4) = 11.
a(6) = 67: 3*23 - 2 = 67; A088878(6) = 23.
(End)

Links

Crossrefs

Cf. A088878, A091179, A091181.
Cf. A136020.

Programs

  • Magma
    [ k: p in PrimesUpTo(1000) | IsPrime(k)  where k is (3*p-2) ]; // K. D. Bajpai, Jun 20 2015
  • Maple
    A091180:= n-> (3*ithprime(n)-2): select(isprime,[seq((A091180(n), n=1..100))]);  # K. D. Bajpai, Jun 20 2015
  • Mathematica
    n = 1; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 500}]; a (* Artur Jasinski, Dec 12 2007 *)
Select[Table[3*Prime[n] - 2,{n, 1000}], PrimeQ] (* K. D. Bajpai, Jun 20 2015 *)
  • PARI
    forprime(p =  1, 1000, k =( 3*p -2); if ( isprime(k), print1(k, ", "))); \\  K. D. Bajpai, Jun 20 2015

Formula

a(n) = 3*A088878(n)-2.

Extensions

Name clarified by Jinyuan Wang, Aug 06 2021

A091179 A088878 indexed by A000040.

Original entry on oeis.org

2, 3, 4, 5, 6, 9, 12, 14, 15, 16, 18, 19, 20, 27, 30, 31, 33, 38, 39, 42, 43, 44, 47, 54, 55, 56, 58, 59, 62, 63, 65, 67, 68, 69, 74, 79, 83, 84, 86, 89, 91, 93, 94, 99, 100, 102, 107, 108, 110, 122, 123, 129, 133, 134, 135, 139, 143, 147, 153, 154, 155, 156, 162, 167
Offset: 1

Views

Author

Ray Chandler, Dec 27 2003

Keywords

Links

Crossrefs

Cf. A088878, A091180, A091181.

Programs

  • Maple
    select(n -> isprime(3*ithprime(n)-2), [$1..1000]); # Robert Israel, Mar 04 2016
  • Mathematica
    PrimePi@ Select[Prime@ Range@ 167, PrimeQ[3 # - 2] &] (* Michael De Vlieger, Mar 04 2016 *)

Formula

a(n)=k such that A000040(k) = A088878(n).

Extensions

Offset corrected by Michael De Vlieger, Mar 04 2016
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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