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.

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A136080 Father primes of order 11.

Original entry on oeis.org

137, 1103, 1931, 2069, 2621, 3449, 3863, 4001, 4139, 5381, 5519, 6761, 8831, 8969, 10211, 13109, 13523, 13799, 15731, 18353, 19319, 21803, 23321, 23459, 25253, 25391, 28151, 28289, 28979, 29531, 29669, 31601, 32429, 32843, 33119, 34361
Offset: 1

Views

Author

Artur Jasinski, Dec 12 2007

Keywords

Comments

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072. For father primes of order 4 see A136073. For father primes of order 5 see A136074. For father primes of order 6 see A136075. For father primes of order 7 see A136076. For father primes of order 8 see A136077. For father primes of order 9 see A136078. For father primes of order 10 see A136079.

Links

Crossrefs

Cf. A023208, A094524, A136019, A136020, A136026, A136027, A136071, A136072, A136073, A136074, A136075, A136076, A136077, A136078, A136079.

Programs

  • Mathematica
    n = 11; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A162337 Primes p such that floor(p/3) is prime.

Original entry on oeis.org

7, 11, 17, 23, 41, 53, 59, 71, 89, 113, 131, 179, 239, 251, 269, 293, 311, 383, 419, 449, 491, 503, 521, 593, 599, 683, 701, 719, 773, 809, 881, 941, 953, 1013, 1049, 1061, 1103, 1151, 1193, 1229, 1259, 1301, 1319, 1373, 1439, 1499, 1511, 1571, 1709, 1733
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 01 2009

Keywords

Comments

Essentially the same as A094524. - R. J. Mathar, Jul 05 2009

Examples

			7 is in the sequence since floor(7/3) = 2 is prime; 89 is in the sequence since floor(89/3) = 29 is prime.

Crossrefs

Cf. A162338. Essentially the same as A094524.

Programs

  • Magma
    [ p: p in PrimesUpTo(1800) | IsPrime(p div 3) ]; // Klaus Brockhaus, Jul 06 2009
  • Mathematica
    lst={};Do[r=Prime[n];If[PrimeQ[p=Floor[r/3]],AppendTo[lst,r]],{n,6!}];lst

Extensions

Edited and listed terms verified by Klaus Brockhaus, Jul 06 2009

A348307 Primes p such that (p-1)/2, (p-2)/3, 2*p+1, 3*p+2 are all prime numbers.

Original entry on oeis.org

23, 21383, 26459, 28643, 111263, 137339, 217643, 333563, 342599, 423323, 486023, 540539, 548519, 567719, 658943, 671039, 755663, 829463, 865499, 890063, 903803, 976883, 1108259, 1168523, 1199183, 1308383, 1316699, 1318379, 1342403, 1349423, 1390199, 1501583, 1503059, 1558079, 1563119
Offset: 1

Views

Author

Marc Morgenegg, Oct 11 2021

Keywords

Comments

For (p-1)/2, those are the safe primes A005385.

Examples

			23 is a term because: (23-1)/2 = 11, (23-2)/3 = 7, 2*23+1 = 47, 3*23+2 = 71, {23, 11, 7, 47, 71} are all prime numbers.

Crossrefs

Cf. A005385 (safe primes).
Intersection of A005385 and A094524 and A005384 and A023208.

Programs

  • Mathematica
    Select[Range[1, 1.5*10^6, 2], AllTrue[{#, (# - 1)/2, (# - 2)/3, 2*# + 1, 3*# + 2}, PrimeQ] &] (* Amiram Eldar, Oct 11 2021 *)
  • PARI
    isok(p) = iferr(isprime(p) && isprime((p-1)/2) && isprime((p-2)/3) && isprime(2*p+1) && isprime(3*p+2), E, 0); \\ Michel Marcus, Oct 11 2021

Extensions

More terms from Michel Marcus, Oct 11 2021
Previous Showing 21-23 of 23 results.

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

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