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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A155897 Square matrix T(m,n)=1 if (2m+1)^n-2 is prime, 0 otherwise; read by antidiagonals.

Original entry on oeis.org

0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0
Offset: 1

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Author

M. F. Hasler, Feb 01 2009

Keywords

Comments

In some sense a "minimal" possible generalization of the pattern of Mersenne primes (cf. A000043) is to consider powers of odd numbers (> 1) minus 2. Since even powers obviously correspond to an odd power of the base squared, it is sufficient to consider only odd powers, cf. A155899.

Crossrefs

Cf. A084714, A128472, A094786, A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.

Programs

  • PARI
    T = matrix( 19,19,m,n, isprime((2*m+1)^n-2)) ;
A155897 = concat( vector( vecmin( matsize(T)), i, vector( i, j, T[j,i-j+1])))

A155898 Square matrix T(m,n)=1 if (2m+1)^(2n)-2 is prime, 0 otherwise; read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1
Offset: 1

Views

Author

M. F. Hasler, Feb 01 2009

Keywords

Comments

In some sense the "minimal" possible generalization of the pattern of Mersenne primes (cf. A000043) is to consider powers of odd numbers minus 2. Here only even powers are considered (which obviously correspond to an odd power of the base squared).

Crossrefs

Cf. A084714, A128472, A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.

Programs

  • PARI
    T = matrix( 19,19,m,n, isprime((2*m+1)^(2*n)-2)) ;
A155898 = concat( vector( vecmin( matsize(T)), i, vector( i, j, T[j,i-j+1])))

A248546 Numbers k such that 75^k - 2 is prime.

Original entry on oeis.org

1, 2, 25, 32, 62, 128, 848, 2091, 2882, 11761, 25915
Offset: 1

Views

Author

Vaclav Kotesovec, Oct 08 2014

Keywords

Comments

Dedicated to N. J. A. Sloane for his 75th birthday!

Crossrefs

Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A376850.

Programs

  • Magma
    [n: n in [0..200] | IsPrime(75^n-2)]; // Vincenzo Librandi, Oct 08 2014
  • Mathematica
    Select[Range[1000],PrimeQ[75^#-2]&]
  • PARI
    is(n)=ispseudoprime(75^n-2) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(10) from Michael S. Branicky, Apr 02 2023
a(11) from Michael S. Branicky, Oct 10 2024

A359695 Numbers k such that 29^k - 2 is prime.

Original entry on oeis.org

2, 4, 8, 14, 42, 420, 1344
Offset: 1

Views

Author

Arsen Vardanyan, Mar 07 2023

Keywords

Comments

a(8) > 10^4, if it exists. - Amiram Eldar, Mar 10 2023
All terms in this sequence are even. - Yifan Xie, Mar 12 2023
a(8) > 5*10^4, if it exists. - Michael S. Branicky, Sep 14 2024

Examples

			4 is a term because 29^4 - 2 = 707279 is a prime number.

Crossrefs

Cf. A087886 (29^k + 2 is prime).
Cf. A128460, A128459, A128457, A109076, A090669, A105772, A109080, (and similar others).

Programs

  • Mathematica
    Select[Range[1400], PrimeQ[29^# - 2] &] (* Amiram Eldar, Mar 10 2023 *)
  • PARI
    is(k) = isprime(29^k - 2);
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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