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.

A120375 Integers k such that 2*5^k - 1 is prime.

Original entry on oeis.org

4, 6, 16, 24, 30, 54, 96, 178, 274, 1332, 2766, 3060, 4204, 17736, 190062, 223536, 260400, 683080
Offset: 1

Views

Author

Walter Kehowski, Jun 28 2006

Keywords

Comments

See comments for A057472. Examined in base 12, all n must be even and all primes must be 1-primes. For example, 1249 is 881 in base 12.
a(16) > 2*10^5. - Robert Price, Mar 14 2015

Examples

			a(1) = 4 since 2*5^4 - 1 = 1249 is the first prime.

Crossrefs

Integers k such that 2*b^k - 1 is prime: A090748 (b=2), A003307 (b=3), this sequence (b=5), A057472 (b=6), A002959 (b=7), A002957 (b=10), A120378 (b=11).
Primes of the form 2*b^k - 1: A000668 (b=2), A079363 (b=3), A120376 (b=5), A158795 (b=7), A055558 (b=10), A120377 (b=11).
Cf. also A000043, A002958.

Programs

  • Magma
    [n: n in [0..2800] |IsPrime(2*5^n - 1)]; // Vincenzo Librandi, Sep 23 2018
  • Maple
    for w to 1 do for k from 1 to 2000 do n:=2*5^k-1; if isprime(n) then printf("%d, %d ",k,n) fi od od;
  • Mathematica
    Select[Range[0, 100], PrimeQ[2*5^# - 1] &] (* Robert Price, Mar 14 2015 *)
  • PARI
    isok(k) = ispseudoprime(2*5^k-1); \\ Altug Alkan, Sep 22 2018

Formula

a(n) = 2*A002958(n).

Extensions

More terms from Ryan Propper, Mar 28 2007
a(14) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 02 2007
a(15) from Robert Price, Mar 14 2015
a(16)-a(18) from Jorge Coveiro and Tyler NeSmith, Jun 14 2020

A120376 Primes of the form 2*5^k - 1.

Original entry on oeis.org

1249, 31249, 305175781249, 119209289550781249, 1862645149230957031249, 111022302462515654042363166809082031249, 25243548967072377773175314089049159349542605923488736152648925781249
Offset: 1

Views

Author

Walter Kehowski, Jun 28 2006

Keywords

Comments

See comments for A057472. Examined in base 12, all n must be even and all primes must be 1-primes. For example, 1249 is 881 in base 12.
The next term has 125 digits. - Harvey P. Dale, Jan 26 2019

Examples

			a(1) = 4 since 2*5^4 - 1 = 1249 is the first prime.

Crossrefs

Integers k such that 2*b^k - 1 is prime: A090748 (b=2), A003307 (b=3), A120375 (b=5), A057472 (b=6), A002959 (b=7), A002957 (b=10), A120378 (b=11).
Primes of the form 2*b^k - 1: A000668 (b=2), A079363 (b=3), this sequence (b=5), A158795 (b=7), A055558 (b=10), A120377 (b=11).
Cf. also A000043, A002958.

Programs

  • Maple
    for w to 1 do for k from 1 to 2000 do n:=2*5^k-1; if isprime(n) then printf("%d, %d",k,n) fi od od;
  • Mathematica
    Select[2*5^Range[100]-1,PrimeQ] (* Harvey P. Dale, Jan 26 2019 *)
  • PARI
    for(k=1, 1e3, if(ispseudoprime(p=2*5^k-1), print1(p, ", "))); \\ Altug Alkan, Sep 22 2018

Formula

a(n) = 2*5^A120375(n) - 1 = 2*5^(2*A002958(n)) - 1. - Jianing Song, Sep 22 2018

A050523 Primes of the form 7*2^k - 1.

Original entry on oeis.org

13, 223, 3583, 917503, 14680063, 3758096383, 246290604621823, 1340933598257652751063553648756520535666396731910651903
Offset: 1

Views

Author

N. J. A. Sloane, Dec 29 1999

Keywords

Links

Crossrefs

See A001771 for more terms.
Cf. A086224, A158795 [Vincenzo Librandi, Mar 28 2009]

Programs

Formula

a(n) = A086224(A001771(n)). - Elmo R. Oliveira, Apr 22 2025

Extensions

13 inserted by R. J. Mathar, Apr 01 2009

A319535 Primes of the form 2*6^k - 1.

Original entry on oeis.org

11, 71, 431, 2591, 15551, 4353564671, 5642219814911, 341163456359156416511, 2046980738154938499071, 20628849596981071092343898111, 26734989077687468135677691953151, 207891275068097752223029732627709951, 269427092488254686881046533485512097791
Offset: 1

Views

Author

Jianing Song, Sep 22 2018

Keywords

Comments

Primes in A164559.
Companion sequence of A057472. There are 49 terms known in this sequence.

Examples

			2*6^1 - 1 = 11, 2*6^2 - 1 = 71, 2*6^3 - 1 = 431, 2*6^4 - 1 = 2591 and 2*6^5 - 1 = 15551 are primes, but 2*6^6 - 1 = 93311 = 23*4057 is not.

Links

Crossrefs

Integers k such that 2*b^k - 1 is prime: A090748 (b=2), A003307 (b=3), A120375 (b=5), A057472 (b=6), A002959 (b=7), A002957 (b=10), A120378 (b=11).
Primes of the form 2*b^k - 1: A000668 (b=2), A079363 (b=3), A120376 (b=5), this sequence (b=6), A158795 (b=7), A055558 (b=10), A120377 (b=11).
Cf. also A000043, A002958, A068231, A164559.

Programs

  • Magma
    [k: n in [1..100] | IsPrime(k) where k is 2*6^n-1];  // K. D. Bajpai, Nov 15 2019
  • Maple
    A319535:= n-> (2*6^n-1): select(isprime, [seq((A319535(n), n=1..200))]);  # K. D. Bajpai, Nov 15 2019
  • Mathematica
    Select[Table[2*6^k-1,{k,1600}], PrimeQ[#]&]  (* K. D. Bajpai, Nov 15 2019 *)
  • PARI
    for(n=1, 99, my(t); if(ispseudoprime(t=2*6^n-1), print1(t", ")))

Formula

a(n) = 2*6^A057472(n) - 1.
Showing 1-4 of 4 results.

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

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