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 11-15 of 15 results.

A220989 a(n) = 12^(2n+1) - 6 * 12^n + 1: the left Aurifeuillian factor of 12^(6n+3) + 1.

Original entry on oeis.org

7, 1657, 247969, 35821441, 5159655937, 743006877697, 106993187463169, 15407021359595521, 2218611104160546817, 319479999339664244737, 46005119908998197280769, 6624737266944778960896001, 953962166440636632998608897
Offset: 0

Views

Author

Stuart Clary, Dec 27 2012

Keywords

Comments

The corresponding right Aurifeuillian factor is A220990.

Links

Crossrefs

Cf. A092440, A085601, A220978, A198410, A220979-A220990.

Programs

  • Mathematica
    Table[12^(2n+1) - 6 * 12^n + 1, {n, 0, 20}]

Formula

Aurifeuillian factorization: 12^(6n+3) + 1 = (12^(2n+1) + 1) * a(n) * A220990(n).
G.f.: -(1008*x^2+558*x+7) / ((x-1)*(12*x-1)*(144*x-1)). [Colin Barker, Jan 03 2013]

A199191 Numbers k such that 3^(2k-3) + 3^(k-1) + 1 is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 10, 11, 41, 83, 160, 178, 526, 881, 2578, 3772, 11873
Offset: 1

Views

Author

Michel Lagneau, Nov 03 2011

Keywords

Comments

Numbers k such that A198410(k) is prime.

Crossrefs

Cf. A198410, A199192.

Programs

  • Mathematica
    Select[Range[250], PrimeQ[((3^(#-1) + 1)^3 -1)/3^#]&]

Extensions

a(16) from Michael S. Branicky, May 12 2023

A199192 Primes of the form 3^(2n-3)+3^(n-1)+1.

Original entry on oeis.org

7, 37, 271, 2269, 19927, 129159847, 1162320517, 49269609804781974450852068861184694669, 589881151426658740854227725580736348850640632297373414091790995505756623268837
Offset: 1

Views

Author

Michel Lagneau, Nov 03 2011

Keywords

Comments

The corresponding n are in A199191.
The next term -- a(10) -- has 152 digits. - Harvey P. Dale, May 28 2015

Crossrefs

Cf. A198410, A199191.

Programs

  • Mathematica
    a={}; Do[p=( (3^(n-1) + 1)^3 -1)/3^n; If[PrimeQ[p], AppendTo[a, p]], {n, 10^2}]; Print[a];
Select[Table[3^(2n-3)+3^(n-1)+1,{n,100}],PrimeQ] (* Harvey P. Dale, May 28 2015 *)

Formula

Primes in A198410.

A220985 The left Aurifeuillian factor of 10^(20n+10) + 1.

Original entry on oeis.org

3541, 904806804901, 99004980069800499001, 9990004998000699800049990001, 999900004999800006999800004999900001, 99999000004999980000069999800000499999000001, 9999990000004999998000000699999800000049999990000001
Offset: 0

Views

Author

Stuart Clary, Dec 27 2012

Keywords

Comments

The corresponding right Aurifeuillian factor is A220986.

Links

Crossrefs

Cf. A092440, A085601, A220978, A198410, A220979-A220990.

Programs

  • Mathematica
    Table[10^(8n+4) - 10^(7n+4) + 5 * 10^(6n+3) - 2 * 10^(5n+3) + 7 * 10^(4n+2) - 2 * 10^(3n+2) + 5 * 10^(2n+1) - 10^(n+1) + 1, {n, 0, 20}]

Formula

a(n) = 10^(8n+4) - 10^(7n+4) + 5 * 10^(6n+3) - 2 * 10^(5n+3) + 7 * 10^(4n+2) - 2 * 10^(3n+2) + 5 * 10^(2n+1) - 10^(n+1) + 1.
Aurifeuillian factorization: 10^(20n+10) + 1 = (10^(4n+2) + 1) * a(n) * A220986(n).

A220986 The right Aurifeuillian factor of 10^(20n + 10) + 1.

Original entry on oeis.org

27961, 1105207205101, 101005020070200501001, 10010005002000700200050010001, 1000100005000200007000200005000100001, 100001000005000020000070000200000500001000001, 10000010000005000002000000700000200000050000010000001
Offset: 0

Views

Author

Stuart Clary, Dec 27 2012

Keywords

Comments

The corresponding left Aurifeuillian factor is A220985.

Links

Crossrefs

Cf. A092440, A085601, A220978, A198410, A220979, A220980, A220981, A220982
Cf. A220983, A220984, A220985, A220987, A220988, A220989, A220990

Programs

  • Mathematica
    a[n_] := 10^(8n + 4) + 10^(7n + 4) + 5 * 10^(6n + 3) + 2 * 10^(5n + 3) + 7 * 10^(4n + 2) + 2 * 10^(3n + 2) + 5 * 10^(2n + 1) + 10^(n + 1) + 1

Formula

a(n) = 10^(8n + 4) + 10^(7n + 4) + 5 * 10^(6n + 3) + 2 * 10^(5n + 3) + 7 * 10^(4n + 2) + 2 * 10^(3n + 2) + 5 * 10^(2n + 1) + 10^(n + 1) + 1
Aurifeuillian factorization: 10^(20n + 10) + 1 = (10^(4n + 2) + 1) * A220985(n) * a(n)
Previous Showing 11-15 of 15 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.