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.

A110056 Least prime that ends a complete Cunningham chain (of the first kind) of length n.

Original entry on oeis.org

13, 7, 167, 4079, 47, 2879, 71850239, 2444789759, 21981381119, 13357981992959, 681004115066879, 1136001594224639, 16756459239477534719, 781558105952602767359
Offset: 1

Views

Author

Alexandre Wajnberg, Sep 04 2005

Keywords

Comments

"Complete" means that this chain is not part of a longer Cunningham chain of the first kind.
Next term is greater than 4*10^17.
A005602(13)-> 8181864863026139 -> ... -> a(13) = 16756459239477534719. [From Washington Bomfim, Oct 21 2009]

Examples

			41->83->167 is a Cunningham chain of the first kind. It is complete because neither (41-1)/2 nor 2*167+1 is prime. It is the first such chain of three primes, so a(3) = 167.

Links

Crossrefs

Cf. A005384, A005385, A007700, A023272, A023302, A023330, A059452, A057326, A059455, A059761, A059762, A059763, A059764, A074313.
Cf. A110059 for Cunningham chains of the second kind.
Cf. A005602 [From Washington Bomfim, Oct 21 2009]

Extensions

Edited and extended by David Wasserman, Aug 08 2006
a(13) and a(14) from Washington Bomfim, Oct 21 2009

A110089 Smallest prime beginning (through <*2+1> or/and <*2-1>) a complete Cunningham chain (of the first or the second kind) of length n.

Original entry on oeis.org

11, 3, 2, 509, 2, 89, 16651, 15514861, 85864769, 26089808579, 665043081119, 554688278429, 758083947856951, 95405042230542329, 69257563144280941
Offset: 1

Views

Author

Alexandre Wajnberg, Sep 04 2005

Keywords

Comments

The word "complete" indicates each chain is exactly n primes long for the operator in function (i.e. the chain cannot be a subchain of another one); and the first and/or last term may be involved in a chain of the other kind (i.e. the chain may be connected to another one). a(1)-a(8) computed by Gilles Sadowski.

Examples

			a(1)=11 because 2, 3, 5 and 7 are included in longer chains than one prime long; and 11 (although included in a <2p+1> chain) has no prime connection through <2p-1>.
a(2)=3 because 3 begins (through 2p+1>) the first complete two primes chain: 3-> 7 (even if 3 and 7 are also part of two others chains, but through <2p-1>).
a(3)=2 because (although 2 begins also a five primes chain through <2p+1>) it begins, through <2p-1>, the first complete three primes chain encountered: 2->3->5.

Links

Crossrefs

Cf. A023272, A023302, A023330, A005384, A005385, A059452, A059455, A007700, A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326, A110059, A110056, A110038, A059766, A110027, A059764, A110025, A110024, A059763, A110022, A109998, A109946, A109927, A109835, A005603.

Formula

a(n) = min(A005602(n), A005603(n)). - R. J. Mathar, Jul 23 2008

Extensions

a(8)-a(13) via A005602, A005603 from R. J. Mathar, Jul 23 2008
a(14)-a(15) via A005602, A005603 from Jason Yuen, Sep 03 2024

A110092 Smallest prime ending (through <*2+1> or <*2-1> separately) a complete Cunningham chain (of the first or the second kind) of length n.

Original entry on oeis.org

17, 59, 73, 4079, 47, 2879, 1065601
Offset: 1

Views

Author

Alexandre Wajnberg, Sep 04 2005

Keywords

Comments

The word "complete" indicates each chain is exactly n primes long for the operator in function (i.e. the chain cannot be a subchain of another one); and the first and/or last term may not be involved in a chain of the other kind (i.e. the chain may not be connected to another one).

Examples

			a(1)=17 because 2, 3, 5, 7, 11 and 13 are part of longer chains whatever the operator; 17 is the first completely isolated prime.
a(2)=59 because it ends the first two primes chain not connected to another one: 29->59.

Links

Crossrefs

Cf. A023272, A023302, A023330, A005384, A005385, A059452, A059455, A007700, Cf. A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326, A110059, A110056, A110038, A059766, A110027, A059764, A110025, A110024, A059763, A110022, A109998, A109946, A109927, A109835, A005603.

Extensions

Terms computed by Gilles Sadowski.

A110093 Smallest prime ending (through <*2+1> or/and <*2-1>) a complete Cunningham chain (of the first or the second kind) of length n.

Original entry on oeis.org

11, 7, 5, 4079, 47, 2879, 1065601
Offset: 1

Views

Author

Alexandre Wajnberg, Sep 04 2005

Keywords

Comments

The word "complete" indicates each chain is exactly n primes long for the operator in function (i.e. the chain cannot be a subchain of another one); but the first and/or last term may be involved in a chain of the other kind (i.e. the chain may be connected to another one).

Examples

			a(1)=11 because 2, 3, 5 and 7 are not ending chains; or are part of chains longer than one prime; 11, although is part of a five primes <2p+1> chain, is isolated through <2p-1>.
a(2)=7 because 7 ends through <2p+1> the first two primes chain: 3->7 (even if both primes are also part of <2p-1> chains).

Links

Crossrefs

Cf. A023272, A023302, A023330, A005384, A005385, A059452, A059455, A007700, Cf. A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326, A110059, A110056, A110038, A059766, A110027, A059764, A110025, A110024, A059763, A110022, A109998, A109946, A109927, A109835, A005603.

Extensions

Terms computed by Gilles Sadowski.
Showing 1-4 of 4 results.

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