A214892 Conway's subprime Fibonacci sequence starting with (4,1).

4, 1, 5, 3, 4, 7, 11, 9, 10, 19, 29, 24, 53, 11, 32, 43, 25, 34, 59, 31, 45, 38, 83, 11, 47, 29, 38, 67, 35, 51, 43, 47, 45, 46, 13, 59, 36, 19, 11, 15, 13, 14, 9, 23, 16, 13, 29, 21, 25, 23, 24, 47, 71, 59, 65, 62, 127, 63, 95, 79, 87, 83, 85, 84, 13, 97, 55, 76, 131, 69, 100, 13, 113

Offset

1,1

Comments

Similar to the Fibonacci recursion starting with (4, 1), but each new nonprime term is divided by its least prime factor. Sequence enters a loop of length 136 after 8 terms on reaching (11, 9).

Links

Wouter Meeussen, Table of n, a(n) for n = 1..144

Richard K. Guy, Tanya Khovanova and Julian Salazar, Conway's subprime Fibonacci sequences, arXiv:1207.5099 [math.NT], 2012-2014.

Mathematica

(* see A214674 *)
a[1] = 4; a[2] = 1; a[n_] := a[n] = If[an = a[n-2]+a[n-1]; PrimeQ[an], an, an/FactorInteger[an][[1, 1]]]; Array[a, 80] (* Jean-François Alcover, Nov 17 2018 *)

Crossrefs

Cf. A000045, A020639, A175723, A214551, A014682, A214674, A214892-A214898.

Sequence in context: A115210 A199150 A329215 * A030352 A212643 A104571

Adjacent sequences: A214889 A214890 A214891 * A214893 A214894 A214895

Keyword

nonn

Author

Wouter Meeussen, Jul 29 2012

Status

approved