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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A126052 Exponents p of the Mersenne primes 2^p - 1 (see A000043) read mod 12.

Original entry on oeis.org

2, 3, 5, 7, 1, 5, 7, 7, 1, 5, 11, 7, 5, 7, 7, 7, 1, 1, 5, 7, 5, 5, 5, 5, 5, 1, 1, 11, 7, 1, 7, 11, 5, 7, 5, 5, 5, 5, 1, 7, 7, 11, 1, 5, 11, 1, 5, 5
Offset: 1

Views

Author

Artur Jasinski, Dec 17 2006

Keywords

Crossrefs

Cf. A000043, A010881, A126043-A126059.

Programs

  • Mathematica
    Mod[MersennePrimeExponent[Range[48]], 12] (* Amiram Eldar, Oct 14 2024 *)

Formula

a(n) = A010881(A000043(n)). - Ivan Panchenko, Apr 07 2018

Extensions

a(45)-a(47) from Ivan Panchenko, Apr 08 2018
a(48) from Amiram Eldar, Oct 14 2024

A126053 Exponents p of the Mersenne primes 2^p - 1 (see A000043) read mod 13.

Original entry on oeis.org

2, 3, 5, 7, 0, 4, 6, 5, 9, 11, 3, 10, 1, 9, 5, 6, 6, 6, 2, 3, 4, 9, 7, 8, 4, 4, 11, 1, 3, 8, 5, 5, 3, 11, 2, 1, 8, 4, 9, 10, 12, 12, 7, 3, 2, 5, 7, 9
Offset: 1

Views

Author

Artur Jasinski, Dec 17 2006

Keywords

Crossrefs

Cf. A000043, A126043-A126059.

Programs

  • Mathematica
    Mod[MersennePrimeExponent[Range[48]], 13] (* Amiram Eldar, Oct 15 2024 *)

Extensions

a(45)-a(47) from Ivan Panchenko, Apr 08 2018
a(48) from Amiram Eldar, Oct 15 2024

A126054 Exponents p of the Mersenne primes 2^p - 1 (see A000043) read mod 14.

Original entry on oeis.org

2, 3, 5, 7, 13, 3, 5, 3, 5, 5, 9, 1, 3, 5, 5, 5, 13, 11, 11, 13, 1, 1, 13, 1, 1, 11, 5, 3, 1, 1, 1, 13, 1, 13, 5, 3, 9, 5, 9, 1, 11, 5, 1, 9, 9, 11, 1, 5
Offset: 1

Views

Author

Artur Jasinski, Dec 17 2006

Keywords

Crossrefs

Cf. A000043, A070696, A126043-A126059.

Programs

  • Mathematica
    Mod[MersennePrimeExponent[Range[47]],14] (* Harvey P. Dale, Aug 12 2021 *)

Formula

a(n) = A070696(A000043(n)). - Michel Marcus, Apr 07 2018

Extensions

a(45)-a(47) from Ivan Panchenko, Apr 08 2018
a(48) from Amiram Eldar, Oct 15 2024

A126055 Exponents p of the Mersenne primes 2^p - 1 (see A000043) read mod 15.

Original entry on oeis.org

2, 3, 5, 7, 13, 2, 4, 1, 1, 14, 2, 7, 11, 7, 4, 13, 1, 7, 8, 13, 14, 11, 8, 2, 11, 4, 7, 8, 13, 4, 1, 14, 8, 7, 14, 11, 2, 8, 7, 1, 13, 11, 7, 2, 2, 1, 14, 11
Offset: 1

Views

Author

Artur Jasinski, Dec 17 2006

Keywords

Crossrefs

Cf. A000043, A167463, A126043-A126059.

Programs

  • Mathematica
    Mod[MersennePrimeExponent[Range[47]],15] (* Harvey P. Dale, Feb 02 2022 *)

Formula

a(n) = A167463(A000043(n)). - Michel Marcus, Apr 07 2018

Extensions

a(45)-a(47) from Ivan Panchenko, Apr 08 2018
a(48) from Amiram Eldar, Oct 15 2024

A126056 Exponents p of the Mersenne primes 2^p - 1 (see A000043) read mod 16.

Original entry on oeis.org

2, 3, 5, 7, 13, 1, 3, 15, 13, 9, 11, 15, 9, 15, 15, 11, 9, 1, 13, 7, 9, 5, 13, 1, 5, 9, 1, 3, 7, 1, 11, 7, 9, 11, 13, 13, 1, 1, 5, 11, 7, 7, 9, 1, 11, 9, 1, 9
Offset: 1

Views

Author

Artur Jasinski, Dec 17 2006

Keywords

Crossrefs

Cf. A000043, A130909, A126043-A126059.

Programs

  • Mathematica
    Mod[MersennePrimeExponent[Range[48]], 16] (* Amiram Eldar, Oct 15 2024 *)

Formula

a(n) = A130909(A000043(n)). - Michel Marcus, Apr 07 2018

Extensions

a(45)-a(47) from Ivan Panchenko, Apr 08 2018
a(48) from Amiram Eldar, Oct 15 2024

A126057 Exponents p of the Mersenne primes 2^p - 1 (see A000043) read mod 17.

Original entry on oeis.org

2, 3, 5, 7, 13, 0, 2, 14, 10, 4, 5, 8, 11, 12, 4, 10, 3, 4, 3, 3, 16, 13, 10, 13, 9, 4, 8, 2, 3, 10, 4, 16, 15, 8, 2, 14, 1, 9, 10, 8, 11, 1, 14, 15, 5, 15, 14, 8
Offset: 1

Views

Author

Artur Jasinski, Dec 17 2006

Keywords

Crossrefs

Cf. A000043, A126043-A126059.

Programs

  • Mathematica
    Array[Mod[MersennePrimeExponent@ #, 17] &, 45] (* Michael De Vlieger, Apr 10 2018 *)

Extensions

a(45)-a(47) from Ivan Panchenko, Apr 09 2018
a(48) from Amiram Eldar, Oct 15 2024

A132192 Least number k such that 4*(k*(2^p-1))^2 + 1 is prime where 2^p-1 is a Mersenne prime (p in A000043).

Original entry on oeis.org

1, 1, 2, 6, 40, 17, 4, 6, 47, 48, 334, 99, 585, 19, 350, 1201, 197, 3577, 2020, 870, 2322, 4488, 6150, 12397, 7817
Offset: 1

Views

Author

Pierre CAMI, Nov 05 2007

Keywords

Examples

			a(1) = 1 since 3 = 2^A000043(1) - 1 and 4*(1*3)^2 + 1 = 37 is prime.

Crossrefs

Cf. A000043, A000668.

Programs

  • Mathematica
    f[n_] := Module[{k = 1}, While[!PrimeQ[4*(k*n)^2 + 1], k++]; k]; f /@ (2^MersennePrimeExponent[Range[15]] - 1)(* Amiram Eldar, Jul 17 2021 *)

Extensions

Data corrected and a(23)-a(25) added by Amiram Eldar, Jul 17 2021

A135701 First differences of indices of A000043.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 3, 7, 6, 4, 3, 67, 13, 96, 121, 11, 116, 128, 19, 594, 30, 131, 897, 181, 156, 2033, 3760, 2105, 1842, 6961, 41453, 7556, 28716, 9974, 108217, 3031, 256669, 402707, 452111, 179537, 113178, 258898, 126198, 263183, 313608, 26616, 833014
Offset: 1

Views

Author

Omar E. Pol, Mar 02 2008

Keywords

Comments

First differences of A016027.
This sequence is related to the perfect numbers A000396 and the Mersenne primes A000668.

Examples

			a(16) = 11 because A000043(16 + 1) = 2281 is the 339 n-th prime, then A016027(16 + 1) = 339 and A000043(16) = 2203 is the 328 n-th prime, then A016027(16) = 328 and we can write 339 - 328 = 11.

Links

Crossrefs

Cf. A000043, A000396, A000668, A000720, A016027.

Programs

  • Mathematica
    Differences@ PrimePi@ Array[MersennePrimeExponent, 45] (* Michael De Vlieger, Dec 18 2017 *)

Formula

a(n) = pi(A000043(n+1)) - pi(A000043(n)), where pi is A000720.
a(n) = A016027(n+1) - A016027(n).

Extensions

a(39) (based on update to A016027) from Ken Takusagawa, May 31 2011
a(40)-a(44) (based on update to A016027) from Patrick J. McNab, Jan 27 2018
a(45)-a(46) from Ivan Panchenko, Apr 12 2018
a(47) from Amiram Eldar, Sep 05 2024

A143387 Least prime a(n) such that M(n)*(M(n)+a(n))-1 and M(n)*(M(n)+a(n))+1 are twin primes with M(i)=i-th Mersenne prime A000043(i).

Original entry on oeis.org

3, 53, 11, 17, 317, 89, 1259, 2543, 7517, 16217, 15107, 33119, 60611, 671063, 2648057
Offset: 1

Views

Author

Pierre CAMI, Aug 11 2008

Keywords

Crossrefs

Cf. A000043, A139426, A143385, A143386.

A163821 a(n) = product of decimal digits of A000043(n).

Original entry on oeis.org

2, 3, 5, 7, 3, 7, 9, 3, 6, 72, 0, 14, 10, 0, 126, 0, 32, 42, 120, 96, 3888, 324, 6, 1701, 0, 0, 4032, 1152, 0, 0, 0, 45360, 12960, 27440, 23328, 3024, 0, 102060, 27216, 0, 0, 97200, 0, 100800, 158760, 0, 0, 67200
Offset: 1

Views

Author

Boris Hostnik (megpplus(AT)siol.net), Aug 04 2009

Keywords

Crossrefs

Cf. A000043, A007954.

Programs

  • Mathematica
    a[n_] := Times @@ IntegerDigits[MersennePrimeExponent[n]]; Array[a, 48] (* Amiram Eldar, Oct 16 2024 *)

Formula

a(n) = A007954(A000043(n)). - Amiram Eldar, Oct 16 2024

Extensions

a(38)-a(39) corrected and a(40)-a(48) added by Amiram Eldar, Oct 16 2024
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