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.

A230769 Numbers k such that (k+1)*2^k - 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 9, 14, 15, 16, 27, 45, 122, 125, 213, 242, 256, 263, 290, 855, 1059, 2273, 3945, 3999, 9512, 14127, 16486, 20056, 28834, 41493, 159147, 227139, 587823
Offset: 1

Views

Author

Zak Seidov, Feb 23 2014

Keywords

Comments

1, 2 and 5 are the only terms of this sequence which are also in A029544. - Gerasimov Sergey, Feb 23 2014
The next term with this property is > 10000. - Michael B. Porter, Feb 23 2014
The probability of a given number N being a twin prime grows like 1/(log(N))^2, so for a given n, the probability that it has this property is 1/n^2, and the sum converges. Are there any n for which n*2^n-1 and n*2^n+1 are both prime? - Michael B. Porter, Feb 25 2014
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 Woodall prime (base 4). These are listed in A086661. In other words, {2*A086661 - 1} gives all the odd terms of this sequence. - Jeppe Stig Nielsen, Oct 16 2019
The largest odd term currently known is 3986381 = 2*A086661(21) - 1. - Jeppe Stig Nielsen, Oct 16 2019

Links

Crossrefs

Cf. A029544, A086661, A196273, A236752.

Programs

Extensions

Edited and extended to values > 2273 by M. F. Hasler, Mar 01 2014
More terms from Jeppe Stig Nielsen, Oct 16 2019

A128001 Numbers k such that (k-1)*2^k + 1 is prime.

Original entry on oeis.org

2, 3, 7, 27, 51, 55, 81, 1471, 1483, 8668, 10885, 20803, 32605, 36391, 57004, 61627, 88651, 89731, 133928, 153428
Offset: 1

Views

Author

N. J. A. Sloane, Jan 25 2008

Keywords

Crossrefs

Cf. A029544, A002064, A196303.

Programs

  • Mathematica
    Select[Range[200], PrimeQ[(# - 1)*2^# + 1] &]  (* G. C. Greubel, May 08 2018 *)
  • PARI
    is(n)=ispseudoprime((n-1)<Charles R Greathouse IV, Jun 06 2017

Extensions

a(8)-a(14) from Jason Earls, Jan 29 2008
a(15)-a(18) from Charles R Greathouse IV, Oct 09 2011
a(19)-a(20) from Michael S. Branicky, May 14 2025

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

A196303 Primes p such that (p-1)*2^p+1 is also prime.

Original entry on oeis.org

2, 3, 7, 1471, 1483, 61627, 88651
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Oct 02 2011

Keywords

Examples

			a(1) = 2 because 2 and (2-1)*2^2 + 1 = 5 are both prime.
a(2) = 3 because 3 and (3-1)*2^3 + 1 = 17 are both prime.
a(3) = 7 because 7 and (7-1)*2^7 + 1 = 769 are both prime.

Crossrefs

Prime terms of A128001.
Cf. A029544, A196421, A196446.

Programs

  • Mathematica
    Select[Prime[Range[9000]],PrimeQ[(#-1)2^#+1]&] (* Harvey P. Dale, Jan 19 2012 *)
  • PARI
    forprime(n=1,1e4,if(ispseudoprime((n-1)<Charles R Greathouse IV, Oct 09 2011

Extensions

a(7) corrected by Michael S. Branicky, May 14 2025
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.