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
Sara Barrows, Emily Noye, Sarah Uttormark, and Matthew Wright, Three's A Crowd: An Exploration of Subprime Tribonacci Sequences, College Math. J. (2023).
Richard K. Guy, Tanya Khovanova and Julian Salazar, Conway's subprime Fibonacci sequences, arXiv:1207.5099 [math.NT], 2012-2014.
Tanya Khovanova, Conway’s Subprime Fibonacci Sequences, Math Blog, July 2012.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
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
KEYWORD
nonn,easy
AUTHOR
Wouter Meeussen, Jul 25 2012
STATUS
approved