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.

A130325 Least prime p such that 3*p*2^n-1 is prime.

Original entry on oeis.org

2, 2, 2, 2, 5, 2, 2, 3, 11, 17, 2, 23, 29, 3, 5, 3, 43, 2, 7, 17, 19, 3, 11, 23, 13, 19, 19, 7, 43, 23, 71, 5, 19, 2, 59, 11, 59, 2, 47, 31, 89, 5, 2, 3, 19, 107, 11, 71, 59, 23, 29, 7, 61, 89, 2, 173, 11, 17, 37, 37, 31, 23, 19, 2, 199, 103, 59, 37, 139, 17, 67, 41, 43
Offset: 0

Views

Author

Pierre CAMI, May 24 2007

Keywords

Examples

			3*2*2^0-1=5 is prime so for n=0 p=2.
3*2*2^1-1=11 is prime so for n=1 p=2.

Links

Crossrefs

Cf. A130326, A130327.

Programs

  • Mathematica
    s={};Do[ i=0;Until[PrimeQ[3Prime[i]*2^n-1],i++];AppendTo[s,Prime[i]] ,{n,0,72}];s (* James C. McMahon, Feb 08 2025 *)
  • PARI
    a(n) = my(p=2); while (!isprime(3*p*2^n-1), p=nextprime(p+1)); p; \\ Michel Marcus, Sep 23 2019

A130326 Least prime p such that 3*p*2^n+1 is prime.

Original entry on oeis.org

2, 2, 3, 3, 2, 2, 3, 2, 19, 5, 5, 2, 5, 11, 3, 47, 7, 2, 11, 19, 47, 11, 11, 59, 97, 11, 23, 5, 11, 2, 31, 13, 37, 3, 53, 2, 71, 5, 5, 97, 2, 7, 3, 3, 5, 167, 41, 37, 5, 163, 23, 73, 31, 17, 59, 19, 29, 41, 73, 43, 59, 47, 71, 3, 109, 2, 11, 3, 79, 41, 13
Offset: 0

Views

Author

Pierre CAMI, May 24 2007

Keywords

Examples

			3*2*2^0+1=7 prime so for n=0 p=2
3*2*2^1+1=13 prime so for n=1 p=2

Links

Crossrefs

Cf. A130325, A130327.

Programs

  • Mathematica
    nn=100;Flatten[Module[{prs=Prime[Range[nn]],c},Table[c=2^n;Select[prs, PrimeQ[ 3c #+1]&,1],{n,0,nn}]]] (* Harvey P. Dale, Sep 01 2013 *)

Extensions

More terms from Harvey P. Dale, Sep 01 2013

A329941 Least prime, p, such that 2*p*3^n - 1 and 2*p*3^n + 1 are twin primes.

Original entry on oeis.org

2, 11, 2, 5, 43, 29, 53, 311, 113, 109, 367, 859, 647, 11, 2, 619, 13, 1051, 157, 2801, 3767, 5, 337, 1721, 3517, 41, 4013, 1879, 1873, 13649, 4637, 2909, 8387, 6521, 1453, 6599, 1277, 4801, 167, 1031, 11213, 4129, 4933, 199, 1427, 859, 9227, 5581, 863, 11959, 10453
Offset: 1

Views

Author

Pierre CAMI, Nov 24 2019

Keywords

Examples

			2*2*3^1 - 1 = 11; 11 and 13 are twin primes so a(1)=2.
2*11*3^2 - 1 = 197; 197 and 199 are twin primes so a(2)=11 as no other prime p < 11 gives twin primes.

Crossrefs

Cf. A130327.

Programs

  • Mathematica
    Array[Block[{p = 2}, While[! AllTrue[2 p 3^# + {-1, 1}, PrimeQ], p = NextPrime@ p]; p] &, 51] (* Michael De Vlieger, Dec 24 2019 *)
  • PARI
    a(n) = {my(p=2); while (!isprime(2*p*3^n - 1) || !isprime(2*p*3^n + 1), p = nextprime(p+1)); p;} \\ Michel Marcus, Nov 25 2019
Showing 1-3 of 3 results.

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

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