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.

User: Paul S. Vanderveen

Paul S. Vanderveen's wiki page.

Paul S. Vanderveen has authored 2 sequences.

A332763 Numbers k such that 6*17^k + 1 is prime.

Original entry on oeis.org

0, 1, 5, 7, 19, 23, 67, 107, 400, 429, 617, 743, 1065, 7717, 12329, 14459, 22425, 114543, 221983, 237453
Offset: 1

Author

Paul S. Vanderveen, Feb 22 2020

Keywords

Comments

a(21) > 3.75*10^5. - Paul S. Vanderveen, Jul 05 2020

Crossrefs

Cf. A141797.

Programs

  • Mathematica
    Select[Range[0, 1000], PrimeQ[6*17^# + 1] &] (* Amiram Eldar, Feb 24 2020 *)
  • PARI
    for(i=1,10000, if( ispseudoprime(6*17^i+1), print1(i, ", ")));

Extensions

a(19) from Paul S. Vanderveen, Mar 09 2020
a(20) from Paul S. Vanderveen, Mar 15 2020

A290283 Primes p such that A215458(p) is prime.

Original entry on oeis.org

3, 5, 7, 11, 17, 19, 23, 101, 107, 109, 113, 163, 283, 311, 331, 347, 359, 701, 1153, 1597, 1621, 2063, 2437, 2909, 3319, 6011, 12829, 46147, 46471, 74219, 112297, 128411, 178693, 223759, 268841, 407821, 526763, 925391, 927763
Offset: 1

Author

Paul S. Vanderveen, Jul 25 2017

Keywords

Comments

Primes p such that (2^p - (1/2 - (i * sqrt(7))/2)^p - (1/2 + (i * sqrt(7))/2)^p + 1)/2 is prime.
It is conjectured that there are infinitely many terms.

Examples

			A215458(3) = 7, A215458(5) = 11, A215458 (7) = 71 are all primes, hence 3, 5, 7 are in this sequence.
		

Crossrefs

Cf. A215458.

Programs

  • Maple
    h := proc(n) option remember; `if`(n=0,2,`if`(n=1,1,h(n-1)-2*h(n-2))) end:
    select(n->isprime((2^n-h(n)+1)/2),select(isprime,[$1..1000])); # Peter Luschny, Jul 26 2017
  • Mathematica
    Function[s, Keys@ KeySelect[s, AllTrue[{#, Lookup[s, #]}, PrimeQ] &]]@ MapIndexed[First[#2] - 1 -> #1 &, LinearRecurrence[{4, -7, 8, -4}, {0, 1, 4, 7}, 7000]] (* Michael De Vlieger, Jul 26 2017 *)
  • PARI
    isprime(([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -4, 8, -7, 4]^n*[0; 1; 4; 7])[1, 1])