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

Author

Wouter Meeussen, Jul 29 2012

Keywords

• nonn

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.

Crossrefs

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

Programs

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 *)