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 1-5 of 5 results.

A002958 Numbers k such that 2*25^k - 1 is prime.

Original entry on oeis.org

2, 3, 8, 12, 15, 27, 48, 89, 137, 666, 1383, 1530, 2102, 8868, 95031, 111768, 130200, 341540
Offset: 1

Views

Author

N. J. A. Sloane, Simon Plouffe

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
  • C. R. Zarnke and H. C. Williams, Computer determination of some large primes, pp. 563-570 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 2, edited R. C. Mullin et al., 1971.

Programs

  • Mathematica
    Do[m = n; If[PrimeQ[2*25^n - 1], Print[n]], {n, 1, 10^3}]
Select[Range[0, 5000], PrimeQ[(2*25^# - 1)] &] (* Vincenzo Librandi, Sep 25 2012 *)
  • PARI
    is(n)=ispseudoprime(2*25^n-1) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(10) from Robert G. Wilson v, Nov 02 2000
a(11)-a(13) from Vincenzo Librandi, Sep 25 2012
a(14)-a(17) (from A120375) from Joerg Arndt, Jun 15 2020
a(18) (from A120375) by Jorge Coveiro, Jun 20 2020

A119591 Least k such that 2*n^k - 1 is prime.

Original entry on oeis.org

1, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 2, 2, 1, 10, 1, 1, 6, 1, 2, 6, 1, 2, 136, 1, 1, 6, 6, 1, 6, 1, 1, 2, 2, 1, 2, 1, 2, 4, 1, 2, 4, 4, 1, 2, 1, 1, 44, 1, 1, 2, 1, 3, 2, 5, 3, 2, 2, 1, 4, 1, 768, 4, 1, 1, 52, 34, 2, 132, 1, 1, 14, 7, 1, 2, 2, 1, 8, 1, 2, 10, 1, 24, 60, 1, 1, 2, 3, 5, 2, 1, 1, 2, 1, 1
Offset: 2

Views

Author

Pierre CAMI, Jun 01 2006

Keywords

Comments

From Eric Chen, Jun 01 2015: (Start)
Conjecture: a(n) is defined for all n.
a(303) > 10000, a(304)..a(360) = {1, 2, 11, 1, 990, 1, 1, 2, 2, 4, 74, 5, 1, 10, 6, 6, 4, 1, 1, 2, 1, 9, 12, 1, 80, 2, 1, 1, 2, 14, 3, 2, 3, 1, 12, 1, 60, 36, 1, 8, 4, 34, 1, 522, 3, 15, 14, 1, 6, 2, 3, 1, 4, 5, 4, 10, 1}.
a(n) = 1 if and only if n is in A006254. (End)
From Eric Chen, Sep 16 2021: (Start)
Now a(303) is known to be 40174, also other terms > 10000: a(383) = 20956, a(515) = 58466, a(522) = 62288, a(578) = 129468, a(581) > 400000, a(590) = 15526, a(647) = 21576, a(662) = 16590, a(698) = 127558, a(704) = 62034, see the a-file and the references.
a(n) = 2 if and only if n is in A066049 but not in A006254.
a(n) = 3 if and only if n is in A214289 but not in A006254 or A066049. (End)

Links

Crossrefs

Cf. A119624, A253178.
Numbers r such that 2*k^r-1 is prime: A090748 (k=2), A003307 (k=3), A146768 (k=4), A120375 (k=5), A057472 (k=6), A002959 (k=7), ... (k=8), ... (k=9), A002957 (k=10), A120378 (k=11), ... (k=12), A174153 (k=13), A273517 (k=14), ... (k=15), ... (k=16), A193177 (k=17), A002958 (k=25).

Programs

  • Mathematica
    f[n_] := Block[{k = 0}, While[ ! PrimeQ[2*n^k - 1], k++ ]; k ]; Table[f[n], {n, 2, 106}] (* Ray Chandler, Jun 08 2006 *)
  • PARI
    a(n) = for(k=1, 2^24, if(ispseudoprime(2*n^k-1), return(k))) \\ Eric Chen, Jun 01 2015

Formula

From Eric Chen, Sep 16 2021: (Start)
a(6*n) = A098873(n).
a(2^n) = A279095(n).
a(A006254(n)) = 1.
a(A066049(n)) <= 2.
a(A214289(n)) <= 3. (End)

Extensions

Corrected and extended by Ray Chandler, Jun 08 2006

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

A058934 Numbers k such that 2*5^k + 1 is prime.

Original entry on oeis.org

0, 1, 3, 13, 45, 105, 159, 297, 1443, 2977, 3699, 11709, 12357, 43165, 121995
Offset: 1

Views

Author

Labos Elemer, Jan 12 2001

Keywords

Comments

a(n) is odd for n > 0. Next term > 17200. - Julián Aguirre, Apr 22 2011
a(16) > 2*10^5. - Robert Price, Mar 14 2015

Examples

			a(3)=13 and 1 + 2*5^13 = 2441406251 is prime.

Crossrefs

Cf. A003306 (2*3^n + 1 is prime), A120375 (2*5^n-1 is prime).

Programs

Extensions

Edited by Joerg Arndt, Apr 22 2011
Terms 1443,...,12357 from Julián Aguirre, Apr 22 2011
a(14)-a(15) from Robert Price, Mar 14 2015

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 1-5 of 5 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.