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.

Previous Showing 11-13 of 13 results.

A248367 Initial members of prime quadruples (n, n+2, n+36, n+38).

Original entry on oeis.org

5, 71, 101, 191, 311, 821, 1451, 4091, 4481, 4931, 5441, 6791, 12071, 13721, 14591, 17921, 18251, 20441, 20771, 20981, 21521, 21611, 35801, 38711, 41141, 41981, 43541, 46271, 47351, 47741, 48821, 49331, 53231, 64151, 70841
Offset: 1

Views

Author

Karl V. Keller, Jr., Jan 11 2015

Keywords

Comments

This sequence is prime n, where there exist two twin prime pairs of (n,n+2), (n+36,n+38).
This sequence is a subsequence of A001359 (lesser of twin primes).
Excluding 5, this sequence is a subsequence of A132232 (primes, 11 mod 30).

Examples

			For n=71, the numbers 71, 73, 107, 109, are primes.

Links

Crossrefs

Cf. A077800 (twin primes), A001359, A132232, A181603 (twin primes, end 1).

Programs

  • Mathematica
    a248367[n_] := Select[Prime@Range@n, And[PrimeQ[# + 2], PrimeQ[# + 36], PrimeQ[# + 38]] &]; a248367[8000] (* Michael De Vlieger, Jan 11 2015 *)
Select[Prime[Range[8000]],AllTrue[#+{2,36,38},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 17 2019 *)
  • Python
    from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+36) and isprime(n+38): print(n,end=', ')

A247089 Initial members of prime quadruples (p, p+2, p+30, p+32).

Original entry on oeis.org

11, 29, 41, 71, 107, 149, 197, 239, 281, 431, 569, 827, 1019, 1031, 1061, 1289, 1451, 1667, 1997, 2081, 2111, 2237, 2309, 2657, 2969, 3299, 3329, 3359, 3527, 3821, 4019, 4127, 4229, 4241, 4517, 5849, 6269, 6659, 6761, 7457, 7559, 8597
Offset: 1

Views

Author

Karl V. Keller, Jr., Jan 10 2015

Keywords

Comments

Primes p such that (p, p+2) and (p+30, p+32) are twin prime pairs.
This sequence is a subsequence of A001359 (lesser of twin primes).
The subset of terms ending in 1 in this sequence is a subsequence of A132232 (primes, 11 mod 30).
The subset of terms ending in 7 in this sequence is a subsequence of A141860 (primes, 2 mod 15).
The subset of terms ending in 9 in this sequence is a subsequence of A132236 (primes, 29 mod 30).

Examples

			For n=11, the numbers 11, 13, 41, 43, are primes.

Links

Crossrefs

Cf. A077800 (twin primes), A001359, A132232, A132236, A141860, A181603 (twins, end 1), A181605 (twins, end 7), A181606 (twins, end 9).

Programs

  • Mathematica
    a247089[n_] := Select[Prime@ Range@ n, And[PrimeQ[# + 2], PrimeQ[# + 30], PrimeQ[# + 32]] &]; a247089[1100] (* Michael De Vlieger, Jan 11 2015 *)
  • Python
    from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+30) and isprime(n+32): print(n,end=', ')

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.

Links

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=', ')
Previous Showing 11-13 of 13 results.

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