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.

Previous Showing 11-16 of 16 results.

A133858 Primes of the form 11^k - 2.

Original entry on oeis.org

14639, 1771559
Offset: 1

Views

Author

Alexander Adamchuk, Sep 27 2007

Keywords

Comments

Last digit of all terms is 9.
The nest term (11^22420-2) is too large to be displayed; see A133982 for the corresponding k. - Joerg Arndt, Nov 28 2020

Examples

			a(1) = 11^4 - 2 = 14639,
a(2) = 11^6 - 2 = 1771559.

Crossrefs

Cf. A104096 (largest prime <= 11^n), A130652, A128472, A084714 (smallest prime of the form (2n-1)^k - 2).
Cf. A014224, A109080, A090669, A128455, A133982, A128457, A128458, A128459, A128460, A128461.

A250200 Least number k>1 such that (2n-1)^k - 2 is prime, or 0 if no such number exists.

Original entry on oeis.org

0, 2, 2, 2, 2, 4, 2, 2, 6, 2, 2, 24, 7, 2, 2, 3, 2, 2, 2, 4, 4, 2, 11, 2, 2, 8, 4, 2, 12, 4, 2, 2, 8, 3, 2, 2, 4, 2, 2, 38, 130, 4, 4, 4, 2, 3, 2, 4, 747, 3, 4, 2, 10, 2, 3, 17, 10, 13, 2, 2, 2, 6, 42, 2, 3, 2, 6, 2, 10, 2, 4, 4, 2, 16, 50, 3, 9, 2, 22, 25
Offset: 1

Views

Author

Robert Price, Mar 02 2015

Keywords

Links

Crossrefs

Cf. A084712, A084713, A084714, A079706, A138066, A255707.

Programs

  • Mathematica
    lst = {0}; For[n = 2, n ≤ 143, n++, For[k = 2, k >= 1, k++, If[PrimeQ[(2*n - 1)^k - 2], AppendTo[lst, k]; Break[]]]]; lst
lnk[n_]:=Module[{k=2,c=2n-1},While[!PrimeQ[c^k-2],k++];k]; Join[{0}, Array[ lnk,80,2]] (* Harvey P. Dale, Jul 24 2017 *)

A155899 Square matrix T(m,n)=1 if (2m+1)^(2n-1)-2 is prime, 0 otherwise; read by antidiagonals.

Original entry on oeis.org

0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0
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 odd powers are considered.

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-1)-2)) ;
A155899 = concat( vector( vecmin( matsize(T)), i, vector( i, j, T[j,i-j+1])))

A133856 Least number k > (2n-1) such that (2n-1)^k - 2 is prime, or 0 if no such number exists.

Original entry on oeis.org

0, 4, 14, 8, 11, 22420, 78, 17, 24, 20, 25, 24, 63, 30, 42, 69, 128, 50, 119, 204, 2816, 76, 52, 288, 64, 66, 184, 153, 67, 268, 78, 210, 438, 295, 96, 74, 136, 128, 2900, 1898, 130, 92, 381, 106, 18626, 97, 98, 1650, 747, 109, 214, 113, 312, 354, 1702, 560, 2798, 123, 171, 554, 11210, 834, 208, 990, 9271
Offset: 1

Views

Author

Alexander Adamchuk, Oct 01 2007

Keywords

Comments

a(66) > 40000. - Robert Price, Mar 02 2015

Links

Crossrefs

Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1), or 0 if no such number exists).
Cf. A084714 (smallest prime of the form (2n-1)^k - 2, or 0 if no such number exists).
Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.
Cf. A133858, A133982.

Formula

A128472(n) = (2n-1)^a(n) - 2 for n > 1.

Extensions

a(6) = 22420 was found by Rick L. Shepherd, Sep 29 2009
a(21)-a(44) from Max Alekseyev, Oct 04 2007
a(45)-a(65) from Robert Price, Mar 02 2015

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

Views

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])))
Previous Showing 11-16 of 16 results.

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