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 1-2 of 2 results.

A175103 Integers n such that 17+30*n are terms in A172456.

Original entry on oeis.org

0, 42, 53, 117, 154, 2377, 3245, 3771, 6381, 9688, 10406, 13879, 13944, 14056, 15026, 18884, 26521, 29565, 30735, 36362, 39310, 43337, 48808, 54415, 58308, 62228, 63378, 69111, 77403, 81750, 86021, 93545, 94388, 103961, 119754, 152555, 162698
Offset: 1

Views

Author

Zak Seidov, Feb 07 2010

Keywords

Crossrefs

Cf. A172456.

Formula

a(n)=(A172456(n)-17)/30.

A252862 Initial members of prime sextuples (n, n+2, n+6, n+8, n+18, n+20).

Original entry on oeis.org

11, 18041, 97841, 165701, 392261, 663581, 1002341, 1068701, 1155611, 1329701, 1592861, 1678751, 1718861, 1748471, 2159231, 2168651, 2177501, 2458661, 2596661, 3215741, 3295541, 3416051, 3919241, 4353311, 5168921, 5201291, 5205461, 6404771
Offset: 1

Views

Author

Karl V. Keller, Jr., Dec 23 2014

Keywords

Comments

This sequence is prime n, where there exist three twin prime pairs of (n,n+2), (n+6,n+8) and (n+18,n+20).
This is a subsequence of A132232 (Primes congruent to 11 mod 30 ).
Also, this is a subsequence of A128467 (30k+11).

Examples

			For n = 18041, the numbers, 18041, 18043, 18047, 18049, 18059, 18061, are primes.
		

Crossrefs

Cf. A077800 (twin primes), A030430 (primes,10*n+1), A132232, A128467, A172456.

Programs

  • Mathematica
    Select[Prime[Range[2500]], Union[PrimeQ[{#, # + 2, # + 6, # + 8, # + 18, # + 20}]] = {True} &] (* Alonso del Arte, Dec 23 2014 *)
    Select[Prime[Range[450000]],AllTrue[#+{2,6,8,18,20},PrimeQ]&] (* Harvey P. Dale, Jun 11 2023 *)
  • PARI
    forprime(p=1,10^7,if(isprime(p+2) && isprime(p+6) && isprime(p+8) && isprime(p+18) && isprime(p+20), print1(p,", "))) \\ Derek Orr, Dec 31 2014
  • Python
    from sympy import isprime
    for n in range(1,10000001,2):
      if isprime(n) and isprime(n+2) and isprime(n+6) and isprime(n+8) and isprime(n+18) and isprime(n+20): print(n,end=', ')
    
Showing 1-2 of 2 results.