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 A214674 Conway's subprime Fibonacci sequence. 14
 1, 1, 2, 3, 5, 4, 3, 7, 5, 6, 11, 17, 14, 31, 15, 23, 19, 21, 20, 41, 61, 51, 56, 107, 163, 135, 149, 142, 97, 239, 168, 37, 41, 39, 40, 79, 17, 48, 13, 61, 37, 49, 43, 46, 89, 45, 67, 56, 41, 97, 69, 83, 76, 53, 43, 48, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Similar to the Fibonacci recursion starting with (1, 1), but each new nonprime term is divided by its least prime factor. Sequence enters a loop of length 18 after 38 terms on reaching (48, 13). REFERENCES Siobhan Roberts, Genius At Play: The Curious Mind of John Horton Conway, Bloomsbury, 2015, pages xx-xxi. LINKS Peter Kagey, Table of n, a(n) for n = 1..250 Richard K. Guy, Tanya Khovanova and Julian Salazar, Conway's subprime Fibonacci sequences, arXiv:1207.5099 [math.NT], 2012-2014. Tanya Khovanova, Conwayâ€™s Subprime Fibonacci Sequences, Math Blog, July 2012. MATHEMATICA guyKhoSal[{a_, b_}] := Block[{c, l, r}, c = NestWhile[(p = Tr[Take[#, -2]]; If[PrimeQ[p], q = p, q = p/Part[FactorInteger[p, FactorComplete -> False], 1, 1]]; Flatten[{#, q}]) &, {a, b}, FreeQ[Partition[#1, 2, 1], Take[#2, -2]] &, 2, 1000]; l = Length[c]; r = Tr@Position[Partition[c, 2, 1], Take[c, -2], 1, 1]; l-r-1; c]; guyKhoSal[{1, 1}] f[s_List] := Block[{a = s[[-2]] + s[[-1]]}, If[ PrimeQ[a], Append[s, a], Append[s, a/FactorInteger[a][[1, 1]] ]]]; Nest[f, {1, 1}, 73] (* Robert G. Wilson v, Aug 09 2012 *) PROG (PARI) fatw(n, a=[0, 1], p=[])={for(i=2, n, my(f=factor(a[i]+a[i-1])~); for(k=1, #f, setsearch(p, f[1, k])&next; f[2, k]--; p=setunion(p, Set(f[1, k])); break); a=concat(a, factorback(f~))); a} fatw(99) /* M. F. Hasler, Jul 25 2012 */ CROSSREFS Cf. A000045, A020639, A175723, A214551, A014682, etc. Cf. A214892-A214898, A282812, A282813, A282814. See also A165911, A272636, A255562, etc. Sequence in context: A117339 A096016 A123274 * A185332 A023818 A102149 Adjacent sequences:  A214671 A214672 A214673 * A214675 A214676 A214677 KEYWORD nonn,easy AUTHOR Wouter Meeussen, Jul 25 2012 STATUS approved

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Last modified August 3 00:25 EDT 2021. Contains 346429 sequences. (Running on oeis4.)