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.

A057472 Numbers k such that 2*6^k - 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 12, 16, 26, 27, 36, 40, 45, 49, 52, 53, 75, 140, 150, 167, 245, 250, 755, 785, 825, 970, 1235, 1289, 1477, 1739, 1872, 1976, 1993, 2175, 4218, 7656, 10898, 13410, 13625, 15706, 33003, 44288, 45556, 48855, 60522, 62795, 98898, 118429, 153714
Offset: 1

Views

Author

Robert G. Wilson v, Sep 10 2000

Keywords

Comments

a(49) > 2*10^5. - Robert Price, Jan 06 2016 [Since a(39) was missing before, this a(49) should actually be a(50). - Jianing Song, Sep 22 2018]
Numbers k such that A164559(k+1) is prime.

Crossrefs

Cf. A164559.

Programs

Extensions

More terms from Pierre CAMI, Jun 16 2006
Edited by Michel Marcus, Jan 06 2012
a(41)-a(48) from Robert Price, Jan 06 2016
Missing a(39) from Pierre CAMI, May 19 2016

A164560 Partial sums of A164532.

Original entry on oeis.org

1, 5, 11, 35, 71, 215, 431, 1295, 2591, 7775, 15551, 46655, 93311, 279935, 559871, 1679615, 3359231, 10077695, 20155391, 60466175, 120932351, 362797055, 725594111, 2176782335, 4353564671, 13060694015, 26121388031, 78364164095
Offset: 1

Views

Author

Klaus Brockhaus, Aug 16 2009

Keywords

Comments

Interleaving of A164559 and A024062 without initial term 0.

Links

Crossrefs

Cf. A164532, A164123 (partial sums of A162436), A164559 (6^n/3-1), A024062 (6^n-1), A026549.

Programs

  • Magma
    T:=[ n le 2 select 3*n-2 else 6*Self(n-2): n in [1..28] ]; [ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..#T]];

Formula

a(n) = 6*a(n-2)+5 for n > 2; a(1) = 1, a(2) = 5.
a(n) = (3-(-1)^n)*6^(1/4*(2*n-1+(-1)^n))/2-1.
G.f.: x*(1+4*x)/((1-x)*(1-6*x^2)).
a(n) = A026549(n) - 1.

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 1-3 of 3 results.

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

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