A083103 -id:A083103 - cp's OEIS frontend

A083216 Fibonacci-like sequence of composite numbers with a(0) = 20615674205555510, a(1) = 3794765361567513.

20615674205555510, 3794765361567513, 24410439567123023, 28205204928690536, 52615644495813559, 80820849424504095, 133436493920317654, 214257343344821749, 347693837265139403, 561951180609961152, 909645017875100555, 1471596198485061707, 2381241216360162262

Offset: 0

Harry J. Smith, Apr 23 2003

a(0) = 20615674205555510, a(1) = 3794765361567513. This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by Herbert S. Wilf in 1990.

Seiichi Manyama, Table of n, a(n) for n = 0..4709 (terms 0..1000 from Alois P. Heinz)
Arturas Dubickas, Aivaras Novikas and Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.
R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag. 37 (1964) 322-324
D. Ismailescu and J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.
Tanya Khovanova, Recursive Sequences
D. E. Knuth, A Fibonacci-Like sequence of composite numbers, Math. Mag. 63 (1) (1990) 21-25
J. W. Nicol, A Fibonacci-like sequence of composite numbers, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.
Herbert S. Wilf, Letters to the Editor, Math. Mag. 63, 284, 1990.
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A000032, A000045, A083103, A083104, A083105, A082411, A221286.

a:= n-> (<<0|1>, <1|1>>^n. <<20615674205555510, 3794765361567513>>)[1, 1]:
seq(a(n), n=0..20);  # Alois P. Heinz, Apr 04 2013

LinearRecurrence[{1,1},{20615674205555510,3794765361567513},25] (* Paolo Xausa, Nov 07 2023 *)

Vec((20615674205555510-16820908843987997*x)/(1-x-x^2)+O(x^9)) \\ Charles R Greathouse IV, Sep 23 2012

a(n) = a(n-1) + a(n-2) for n>1.

G.f.: (20615674205555510-16820908843987997*x)/(1-x-x^2).

A083104 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 331635635998274737472200656430763, 1510028911088401971189590305498785.

Original entry on oeis.org

331635635998274737472200656430763, 1510028911088401971189590305498785, 1841664547086676708661790961929548, 3351693458175078679851381267428333, 5193358005261755388513172229357881, 8545051463436834068364553496786214

Offset: 0

Harry J. Smith, Apr 23 2003

This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by Ronald Graham in 1964.

Indranil Ghosh, Table of n, a(n) for n = 0..4618
Arturas Dubickas, Aivaras Novikas and Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.
R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag. 37 (1964) 322-324.
D. Ismailescu and J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.
Tanya Khovanova, Recursive Sequences
D. E. Knuth, A Fibonacci-Like sequence of composite numbers, Math. Mag. 63 (1) (1990) 21-25
J. W. Nicol, A Fibonacci-like sequence of composite numbers, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.
Carlos Rivera, Problem 31. Fibonacci- all composites sequence, The Prime Puzzles and Problems Connection.
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083105, A083216, A082411, A221286.

LinearRecurrence[{1,1},{331635635998274737472200656430763,1510028911088401971189590305498785},7] (* Harvey P. Dale, Oct 29 2016 *)

a(n)=331635635998274737472200656430763*fibonacci(n-1)+ 1510028911088401971189590305498785*fibonacci(n) \\ Charles R Greathouse IV, Dec 18 2014

G.f.: (331635635998274737472200656430763+1178393275090127233717389649068022*x)/(1-x-x^2). - Colin Barker, Jun 19 2012

Name clarified by Robert C. Lyons, Feb 07 2025

A083105 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 62638280004239857, 49463435743205655.

Original entry on oeis.org

62638280004239857, 49463435743205655, 112101715747445512, 161565151490651167, 273666867238096679, 435232018728747846, 708898885966844525, 1144130904695592371, 1853029790662436896, 2997160695358029267, 4850190486020466163, 7847351181378495430

Offset: 0

Harry J. Smith, Apr 23 2003

a(0) = 62638280004239857, a(1) = 49463435743205655. This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by D. E. Knuth in 1990.

Seiichi Manyama, Table of n, a(n) for n = 0..4705
Arturas Dubickas, Aivaras Novikas and Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.
R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag. 37 (1964) 322-324.
D. Ismailescu and J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.
Tanya Khovanova, Recursive Sequences
D. E. Knuth, A Fibonacci-like sequence of composite numbers, Math. Mag. 63 (1) (1990) 21-25.
J. W. Nicol, A Fibonacci-like sequence of composite numbers, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.
Carlos Rivera, Problem 31. Fibonacci- all composites sequence, The Prime Puzzles and Problems Connection.
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083216, A082411, A221286.

a:= n-> (<<0|1>, <1|1>>^n. <<62638280004239857, 49463435743205655>>)[1, 1]:
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 20 2021

LinearRecurrence[{1,1},{62638280004239857,49463435743205655},20] (* Paolo Xausa, Nov 07 2023 *)

G.f.: (62638280004239857-13174844261034202*x)/(1-x-x^2). [Colin Barker, Jun 19 2012]

Name clarified by Robert C. Lyons, Feb 07 2025

A082411 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 407389224418, 76343678551.

Original entry on oeis.org

407389224418, 76343678551, 483732902969, 560076581520, 1043809484489, 1603886066009, 2647695550498, 4251581616507, 6899277167005, 11150858783512, 18050135950517, 29200994734029, 47251130684546, 76452125418575, 123703256103121, 200155381521696, 323858637624817

Offset: 0

Harry J. Smith, Apr 23 2003

a(0) = 407389224418, a(1) = 76343678551. This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by John Nicol in 1999.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Arturas Dubickas, Aivaras Novikas and Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.
R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag. 37 (1964) 322-324.
D. Ismailescu and J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.
Tanya Khovanova, Recursive Sequences
D. E. Knuth, A Fibonacci-Like sequence of composite numbers, Math. Mag. 63 (1) (1990) 21-25
J. W. Nicol, A Fibonacci-like sequence of composite numbers, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.
Herbert S. Wilf, Letters to the Editor Math. Mag. 63, 284, 1990.
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083105, A083216, A221286.

a:= n-> (<<0|1>, <1|1>>^n. <<407389224418, 76343678551>>)[1, 1]:
seq(a(n), n=0..20);  # Alois P. Heinz, Apr 04 2013

LinearRecurrence[{1,1},{407389224418,76343678551},25] (* Paolo Xausa, Nov 07 2023 *)

G.f.: (407389224418-331045545867*x)/(1-x-x^2). [Colin Barker, Jun 19 2012]

Name clarified by Robert C. Lyons, Feb 07 2025

cp's OEIS Frontend

A083216 Fibonacci-like sequence of composite numbers with a(0) = 20615674205555510, a(1) = 3794765361567513.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A083104 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 331635635998274737472200656430763, 1510028911088401971189590305498785.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A083105 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 62638280004239857, 49463435743205655.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A082411 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 407389224418, 76343678551.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions