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.

A064812 Smallest prime p such that the infinite sequence {p, p'=2p-1, p''=2p'-1, ...} begins with a string of exactly n primes.

Original entry on oeis.org

5, 3, 2, 2131, 1531, 33301, 16651, 15514861, 857095381, 205528443121, 1389122693971, 216857744866621, 758083947856951, 107588900851484911, 69257563144280941
Offset: 1

Views

Author

David Terr, Oct 21 2002

Keywords

Comments

Chains of length n of nearly doubled primes.
Smallest prime beginning a complete Cunningham chain of length n of the second kind. (For the first kind see A005602.) - Jonathan Sondow, Oct 30 2015

Examples

			a(3) = 2 because 2 is the smallest prime such that the sequence {2, 3, 5, 9, ...} begins with exactly 3 primes, where each term in the sequence is twice the preceding term minus 1.

Links

Crossrefs

A better version of A005603.
Cf. (A005382 and A005383), A057326, A057327, A057328, A057329, A057330, A005602.
Cf. A002808, A006450, A049076-A049081, A050436, A076237-A076239, A050436-A050439, A065860, A181697, A263879.

A076236 a(n) = A050435(n) mod A002808(n).

Original entry on oeis.org

1, 0, 7, 7, 8, 9, 10, 10, 10, 10, 12, 12, 12, 12, 13, 13, 13, 14, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 19, 19, 19, 20, 20, 20, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 27, 28, 28, 28, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 32
Offset: 1

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Comments

Original name: Remainder when 2nd order composite, A050435(n), is divided by first order composite, A002808(n). - Michael De Vlieger, Dec 09 2018

Examples

			Let c(n) be the n-th composite number. a(1) = 1 since c(c(1)) mod c(1) = c(4) mod 4 = 9 mod 4 = 1. a(2) = 0 since c(c(2)) mod c(2) = c(6) mod 6 = 12 mod 6 = 0. - _Michael De Vlieger_, Dec 09 2018

Links

Crossrefs

Cf. A002808, A050435-A050439, A065860, A076237-A076239.

Programs

Formula

a(n) = A050435(n) mod A002808(n).

Extensions

Edited by Michael De Vlieger, Dec 09 2018

A076237 a(n) = A050435(n) mod n.

Original entry on oeis.org

0, 0, 0, 0, 3, 3, 3, 1, 8, 8, 10, 9, 8, 8, 8, 7, 6, 6, 7, 8, 7, 6, 5, 4, 5, 4, 3, 4, 5, 4, 3, 4, 3, 2, 2, 2, 2, 1, 0, 0, 40, 0, 0, 43, 43, 44, 44, 45, 45, 45, 47, 48, 49, 50, 50, 50, 53, 53, 53, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 57, 58, 59, 59, 60, 62, 63, 63, 64, 65, 65, 65, 67
Offset: 1

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Crossrefs

Cf. A002808, A050435-A050439, A065860, A076236-A076239.

Programs

  • Mathematica
    Module[{cmps=Select[Range[300],CompositeQ],c2},c2=Table[cmps[[cmps[[n]]]],{n,100}];Mod[#[[1]],#[[2]]]&/@Thread[{c2,Range[Length[c2]]}]] (* Harvey P. Dale, May 02 2022 *)

Formula

a(n) = Mod[cc[n], n] = Mod[A050435(n), n]

A076238 a(n) = A050436(n) mod A002808(n).

Original entry on oeis.org

0, 3, 1, 8, 8, 9, 8, 8, 7, 6, 8, 7, 6, 4, 5, 4, 3, 4, 4, 4, 3, 2, 2, 2, 1, 0, 0, 0, 43, 43, 44, 45, 45, 45, 47, 48, 50, 50, 50, 53, 53, 55, 55, 55, 55, 56, 56, 56, 56, 56, 58, 59, 60, 62, 63, 63, 65, 65, 65, 68, 68, 68, 68, 68, 69, 69, 69, 69, 70, 70, 72, 72, 73, 74, 74, 76, 78, 78
Offset: 1

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Crossrefs

Cf. A002808, A050435-A050439, A065860, A076236-A076239.

Formula

a(n)=Mod[ccc[n], c[n]]=Mod[A050436(n), A002808[n]]
Showing 1-4 of 4 results.

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