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.

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A292937 a(0)=1, followed by highly safe primes: positions of records in A292936.

Original entry on oeis.org

1, 2, 5, 11, 23, 47, 2879, 71850239, 2444789759, 21981381119
Offset: 0

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Author

Antti Karttunen, Sep 28 2017

Keywords

Comments

The starting offset is 0 to accommodate 1, which is only nonprime in this sequence, and also to align with the indexing used in A110056.
Sequence starts like A007505, and at least for terms a(5) .. a(9) is equal to A110056.

Crossrefs

Cf. A007505, A066174, A110056, A292936.
Cf. A000040, A005385, A066179, A157358, A157359 (each starts with the term a(1) .. a(5) of this sequence).

Programs

  • Mathematica
    With[{s = Table[SelectFirst[Range[0, 10], ! PrimeQ@ Floor[n/(2^#)] &], {n, 10^7}]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Sep 29 2017 *)

A332549 Numbers k such that A332547(k) = 3.

Original entry on oeis.org

5, 6, 8, 11, 12, 23, 47, 96, 191, 192, 383, 768, 6143, 12288, 786431, 786432, 3221225472, 51539607551, 206158430208, 824633720831, 6597069766656, 26388279066623, 108086391056891903, 55340232221128654847, 221360928884514619392, 226673591177742970257407
Offset: 1

Views

Author

N. J. A. Sloane, Feb 21 2020

Keywords

Comments

The numbers k such that A332547(k) = 1 are given by A068194, a sequence of interest to Mersenne and Fermat, so this sequence may also be interesting.
The factors of the initial terms are 5, 2*3, 2^3, 11, 2^2*3, 23, 47, 2^5*3, 191, 2^6*3, 383, 2^8*3, 6143, 2^12*3, 786431, 2^18*3, ...
There are essentially two cases. Firstly n can be an odd prime and n+1 of the form 3*2^k. These are the terms of A007505 with 2 excluded. Otherwise n can be of the form 3*2^k and n+1 a prime. These are 1 less than the terms of A039687. In addition, 8 is a term which is a special case. - Andrew Howroyd, Feb 21 2020

Crossrefs

Cf. A007505, A039687, A068194, A332547.

Programs

  • PARI
    upto(n)={Set(concat([if(n<8,[],[8]), select(isprime, [3*2^k-1 |k<-[1..logint((n+1)\3, 2)]]), select(p->isprime(p+1), [3*2^k |k<-[1..logint(n\3, 2)]])]))} \\ Andrew Howroyd, Feb 21 2020

Extensions

Terms a(17) and beyond from Andrew Howroyd, Feb 21 2020

A195530 Primes of the form 3*2^n - 2*n - 1.

Original entry on oeis.org

2, 3, 7, 17, 179, 751, 6121, 12263, 49123, 393181, 50331599, 201326539, 13194139533227, 56668397794435742564203, 1856910058928070412348686157, 8769009823985417509222108996297698117935595257533, 4597486622597666575075041081450927550856217366550806167
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Sep 21 2011

Keywords

Comments

Generated by n = 0, 1, 2, 3, 6, 8, 11, 12, 14, 17, 24, 42, 74, 89, 161, 180,...

Crossrefs

Cf. A005408, A007505, A007283.

Programs

  • Mathematica
    Select[Table[3 2^n-2n-1,{n,0,200}],PrimeQ] (* Harvey P. Dale, May 24 2012 *)

Formula

prime: A007283(n)-A005408(n).

A267943 Numbers n such that 2^n - 3 and 3*2^n - 1 are both prime.

Original entry on oeis.org

3, 4, 6, 94
Offset: 1

Views

Author

Arkadiusz Wesolowski, Jan 22 2016

Keywords

Comments

The intersection of A002235 and A050414 is not empty (3 does not belong to A267985).

Examples

			a(3) = 6 because 2^6 - 3 = 61 and 3*2^6 - 1 = 191 are both prime.

Crossrefs

Cf. A002235, A007505, A050414, A050415, A238694, A267985.

Programs

  • Magma
    [n: n in [2..94] | IsPrime(2^n-3) and IsPrime(3*2^n-1)];
  • PARI
    isok(n) = isprime(2^n-3) && isprime(3*2^n-1);

Formula

A002235 INTERSECT A050414.
Previous Showing 11-14 of 14 results.

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

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