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 1-4 of 4 results.

A029544 Near Cullen numbers: k such that (k+1)*2^k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 5, 6, 13, 26, 65, 66, 86, 114, 133, 186, 294, 445, 866, 1325, 1478, 1823, 2765, 7553, 7943, 10178, 20960, 20964, 21337, 26562, 85374, 96749, 247038
Offset: 1

Views

Author

Henri Lifchitz

Keywords

Comments

Primes in the sequence are 2, 5, 13, 1823, 96749, ... - R. J. Mathar, Oct 15 2011
We can write (k+1)*2^k + 1 = {(k+1)/2}*4^{(k+1)/2} + 1, and when k is odd, this takes the form of a generalized Cullen prime (base 4). These are listed in A007646. In other words, {2*A007646 - 1} gives all the odd terms of this sequence. - Jeppe Stig Nielsen, Oct 16 2019

Links

Crossrefs

Cf. A002064, A007646, A230769.

Programs

  • PARI
    isok(n) = isprime((n+1)*2^n+1); \\ Michel Marcus, Nov 09 2013

Extensions

Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

A236752 Primes of the form k*2^(k-1) - 1.

Original entry on oeis.org

3, 11, 31, 79, 191, 5119, 245759, 524287, 1114111, 3758096383, 1618481116086271, 653980173926178609468673073657929531391, 5359447279004780799548150067050349330431
Offset: 1

Views

Author

Gerasimov Sergey, Jan 30 2014

Keywords

Comments

Primes in A087323.
Corresponding values of k: 2, 3, 4, 5, 6, 10, 15, 16, 17, 28, 46, 123, ...
The values of k-1 are listed in A230769. - Jeppe Stig Nielsen, Oct 16 2019

Examples

			79 is in this sequence because it is prime and for k = 5, k*2^(k-1) - 1 = 5*2^(5-1) - 1 = 79.

Crossrefs

Cf. A002054, A003261, A196273, A230769.

Extensions

More terms and corrections of terms and comments by Ralf Stephan, Feb 03 2014

A196273 Primes of the form n*2^(n-1)+1.

Original entry on oeis.org

2, 5, 13, 193, 449, 114689, 1811939329, 2434970217729660813313, 4943727411754159833089, 6731298963614255244763987969, 2388456554926020709124028311441244161
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Sep 29 2011

Keywords

Comments

Generated by n = 1, 2, 3, 6, 7, 14, 27, 66, 67, 87, 115, .. = A029544(n)+1.
See also A236752 for primes of the form k*2^(k-1) - 1, and A230769 for the corresponding indices k (minus 1). - M. F. Hasler, Mar 01 2014

Crossrefs

Cf. A005183.

Programs

  • Mathematica
    Select[Table[n*2^(n-1)+1,{n,150}],PrimeQ] (* Harvey P. Dale, Jul 17 2018 *)
  • PARI
    lista(nn) = {for (n=1, nn, if (isprime(p = n*2^(n-1)+1), print1(p, ", ")););} \\ Michel Marcus, Nov 09 2013

A237251 Primes p such that p*2^(p-1)-1 is prime.

Original entry on oeis.org

2, 3, 5, 17, 257, 16487
Offset: 1

Views

Author

Gerasimov Sergey, Feb 05 2014

Keywords

Comments

The fifth Fermat prime, 65537, is not in the sequence: 65537*2^65536-1 is composite (per PFGW). - Michael B. Porter, Feb 11 2014
Also 65537*2^65536-1 is divisible by 16267 and 2058772459. - Jeppe Stig Nielsen, Jan 04 2020

Crossrefs

Cf. A019434, A092506, A230769, A236752.

Programs

  • PARI
    isok(p) = isprime(p) && isprime(p*2^(p-1) - 1); \\ Michel Marcus, Feb 06 2014

Extensions

a(5) from Ralf Stephan, Feb 03 2014
a(6) = A230769(26)+1 appended by Jeppe Stig Nielsen, Jan 04 2020
Showing 1-4 of 4 results.

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

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