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 1-4 of 4 results.

A121370 Least number k such that (k*M(n))^2 + k*M(n) - 1 is prime with M(i)=i-th Mersenne prime.

Original entry on oeis.org

1, 3, 1, 7, 8, 19, 13, 4, 16, 3, 42, 24, 434, 84, 160, 579, 475, 529, 2450, 2644, 3928, 558, 13680, 7146, 1408, 3003, 2369, 55000, 83873
Offset: 1

Views

Author

Pierre CAMI, Jul 24 2006

Keywords

Examples

			M(4)=2^7-1=127
127^2+127-1=16255 composite
(2*127)^2+2*127-1=64769 composite
(3*127)^2+3*127-1=145541 composite
(4*127)^2+4*127-1=258571 composite
(5*127)^2+5*127-1=403859 composite
(6*127)^2+6*127-1=581405 composite
(7*127)^2+7*127-1=791209 prime so k(4)=7
1*(2^2-1)*(1*(2^2-1)+1)-1=11 prime, 2^2-1 first Mersenne prime, a(1)=1.
3*(2^3-1)*(3*(2^3-1)+1)-1=461 prime, 2^3-1 second Mersenne prime, a(2)=3.
n=6: Mp(6) = 131071 and 19*131071*(19*131071 + 1) - 1 = 6201840632149 which is prime, and for k=1..18 no prime appears. - _Wolfdieter Lang_, Oct 26 2014

Crossrefs

Cf. A121371.
Cf. A000043 (Mersenne exponents), A000668 (Mersenne primes).
Cf. A137906, A137907, A137909.

Programs

  • PARI
    lista() = {v = readvec("b000043.txt"); for (i=1, #v, mp = 2^v[i] - 1; k=1; while (!isprime(k*mp*(k*mp + 1) - 1), k++); print1(k, ", "););} \\ Michel Marcus, Oct 27 2014

Formula

a(n) is the least k >= 1 for which k*Mp(n)*(k*Mp(n) + 1) - 1 is prime, where Mp(n) = A000668(n) (see Name). - Wolfdieter Lang, Oct 26 2014

Extensions

a(21) corrected by Pierre CAMI, Mar 04 2014
a(27)-a(29) by Pierre CAMI, Oct 11 2014
Checked for n = 1..15 by Wolfdieter Lang, Oct 26 2014
Merged with A137908 by Vaclav Kotesovec, Oct 30 2014

A137906 Least k such that k*(2^p-1)*(k*(2^p-1)-1)-1 is prime, where 2^p-1 runs through the Mersenne primes.

Original entry on oeis.org

1, 1, 1, 1, 1, 4, 1, 27, 14, 34, 6, 132, 97, 1, 500, 1816, 1292, 136, 2445, 15, 1934, 5472, 1584, 2734, 21022, 5870
Offset: 1

Views

Author

Pierre CAMI, Feb 22 2008

Keywords

Examples

			1*(2^2-1)*(1*(2^2-1)-1)-1=5 prime, 2^2-1 first Mersenne prime, a(1)=1;
1*(2^3-1)*(1*(2^3-1)-1)-1=41 prime, 2^3-1 second Mersenne prime, a(2)=1.

Crossrefs

Cf. A137907, A137908, A137909.

A137907 Least k such that k*(2^p-1)*(k*(2^p-1)-1)+1 is prime, where 2^p-1 runs through the Mersenne primes.

Original entry on oeis.org

1, 1, 9, 6, 9, 24, 4, 7, 28, 70, 73, 121, 511, 106, 343, 2169, 1423, 2146, 5736, 4444, 2484, 2310, 2679, 25623, 2481, 39213
Offset: 1

Views

Author

Pierre CAMI, Feb 22 2008

Keywords

Examples

			1*(2^2-1)*(1*(2^2-1)-1)+1=7 prime, 2^2-1 first Mersenne prime, a(1)=1;
1*(2^3-1)*(1*(2^3-1)-1)+1=43 prime, 2^3-1 second Mersenne prime, a(2)=1.

Crossrefs

Cf. A137906, A137908, A137909.

Extensions

Corrected by Pierre CAMI, Jun 16 2012

A249509 Smallest number k >= A000043(n) such that k*A000668(n)*(k*A000668(n)+1)-1 is prime.

Original entry on oeis.org

2, 3, 5, 7, 25, 19, 20, 42, 96, 190, 134, 164, 650, 852, 1455, 2765, 2480, 3960, 5464, 6694, 17206, 13118, 13680, 28481, 27445, 28821, 101696, 116232, 142083, 187376, 250118, 1200007
Offset: 1

Views

Author

Pierre CAMI, Oct 30 2014

Keywords

Comments

a(34) = 1200007.
A000043(34) = 756839.
A000668(34) = 2^756839-1.
1200007*(2^756839-1)*(1200007*(2^756839-1)+1)-1 is a 455675 digits certified prime using PFGW.

Links

Crossrefs

Cf. A000043, A000668, A137908, A137909.
Showing 1-4 of 4 results.

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