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.

A378134 a(n) is the smallest prime p such that (2*p)^(2^n) + 1 is also prime.

Original entry on oeis.org

2, 2, 2, 2, 37, 281, 137, 2129, 139, 23, 1231, 1279, 17477
Offset: 0

Views

Author

Juri-Stepan Gerasimov, Nov 17 2024

Keywords

Crossrefs

Primes p such that (2*p)^(2^k) + 1 is prime: A005384 (k = 0), A052291 (k = 1), A378146 (k = 2).
If a(n) is the smallest prime number p such that (p*2^m)^(2^n) + 1, then we have:
2, 2, 2, 2, 2 (in case m = 0), where primes of the form (p*2^0)^(2^n)+1 are A019434;
this sequence (in case m = 1).
Cf. A378143.

Extensions

a(11)-a(12) from Michael S. Branicky, Nov 18 2024

A378146 Primes p such that 16*p^4 + 1 is prime.

Original entry on oeis.org

2, 3, 17, 23, 37, 41, 53, 59, 71, 97, 127, 139, 167, 233, 263, 277, 283, 379, 389, 457, 521, 563, 571, 601, 619, 661, 691, 743, 797, 809, 811, 823, 853, 859, 877, 967, 971, 997, 1051, 1063, 1103, 1187, 1277, 1289, 1321, 1367, 1399, 1433, 1451, 1499
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 17 2024

Keywords

Crossrefs

Primes p such that (2*p)^(2^k) + 1 is prime: A005384 (k = 0), A052291 (k = 1), this sequence (k = 2).
Cf. A378134, A378143.

Programs

  • Magma
    [p: p in PrimesUpTo(1500) | IsPrime(16*p^4+1)];
  • Mathematica
    Select[Prime[Range[250]], PrimeQ[16*#^4 + 1] &] (* Amiram Eldar, Nov 17 2024 *)
  • PARI
    list(lim)=my(v=List()); forprime(p=2,lim, if(isprime(16*p^4+1), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Nov 17 2024

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Nov 17 2024

A378702 Primes p such that 256*p^8 + 1 is prime.

Original entry on oeis.org

2, 59, 271, 281, 433, 467, 587, 971, 1039, 1097, 1181, 1277, 1283, 1361, 1373, 1427, 1447, 1481, 1579, 1657, 1777, 2089, 2129, 2269, 2381, 2617, 2753, 2803, 2939, 3181, 3319, 3691, 3823, 4093, 4217, 4241, 4327, 4909, 4999, 5279, 5303, 5387, 5483, 6043, 6121, 6197, 6221, 6563, 6577, 7159, 7243, 7867
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 04 2024

Keywords

Crossrefs

Primes p such that (2*p)^(2^n) + 1 is prime: A005384 (n = 0), A052291 (n = 1), A378146 (n = 2), this sequence (n = 3).
Cf. A006314, A378134, A378143.

Programs

  • Magma
    [p: p in PrimesUpTo(8000) | IsPrime(256*p^8 + 1)];
  • Mathematica
    Select[Prime[Range[1000]], PrimeQ[(2*#)^8 + 1] &] (* Amiram Eldar, Dec 06 2024 *)
  • PARI
    select(p->isprime(256*p^8+1), primes(10^6)) \\ Charles R Greathouse IV, Dec 04 2024

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Dec 04 2024
Showing 1-3 of 3 results.

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

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