OFFSET
1,1
COMMENTS
Conjecture: each term > 3 of the sequence is the greater member of a twin prime pair (A006512).
Indices of the records are 1, 2, 4, 6, 9, 10, 15, 18, 21, 25, 28, 30, 38, 72, 90, ... [R. J. Mathar, Nov 05 2009]
One can formulate a similar conjecture without verification of the primality of the terms (see Conjecture 4 in my paper). [Vladimir Shevelev, Nov 13 2009]
LINKS
E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol.11 (2008), Article 08.2.8.
E. S. Rowland, A natural prime-generating recurrence, arXiv:0710.3217 [math.NT], 2007-2008.
V. Shevelev, A new generator of primes based on the Rowland idea, arXiv:0910.4676 [math.NT], 2009.
V. Shevelev, Three theorems on twin primes, arXiv:0911.5478 [math.NT], 2009-2010. [Vladimir Shevelev, Dec 03 2009]
MATHEMATICA
nxt[{n_, a_}] := {n + 1, If[EvenQ[n], a + GCD[n+1, a], a + GCD[n-1, a]]};
A167494 = DeleteCases[Differences[Transpose[NestList[nxt, {1, 2}, 10^7]][[2]]], 1];
Tally[A167494][[All, 1]] //. {a1___, a2_, a3___, a4_, a5___} /; a4 <= a2 :> {a1, a2, a3, a5} (* Jean-François Alcover, Oct 29 2018, using Harvey P. Dale's code for A167494 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Vladimir Shevelev, Nov 05 2009
EXTENSIONS
Simplified the definition to include all records; one term added by R. J. Mathar, Nov 05 2009
a(16) to a(21) from R. J. Mathar, Nov 19 2009
a(22) from Jean-François Alcover, Oct 29 2018
STATUS
editing