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%I #22 Nov 03 2018 12:17:56
%S 2,3,7,13,43,139,313,661,1321,2659,5419,10891,22039,44383,88801,
%T 177841,355723,713833,1427749,2860771,5725453,11461141,22933441,
%U 45895573,91793059,183616423,367232911,734482123,1468965061,2937930211,5875882249,11751795061,23503590559,47007181621,94014363763
%N Records of first differences of A166944.
%C Conjecture. Each term of the sequence is the greater of a pair of twin primes (A006512).
%H E. S. Rowland, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Rowland/rowland21.html">A natural prime-generating recurrence</a>, Journal of Integer Sequences, Vol.11(2008), Article 08.2.8. arXiv:<a href="https://arxiv.org/abs/0710.3217">0710.3217</a> [math.NT]
%H V. Shevelev, <a href="https://arxiv.org/abs/0910.4676">An infinite set of generators of primes based on the Rowland idea and conjectures concerning twin primes</a>, arXiv:0910.4676 [math.NT], 2009.
%H V. Shevelev, <a href="https://arxiv.org/abs/0911.5478">Three theorems on twin primes</a>, arXiv:0911.5478 [math.NT], 2009-2010.
%t Reap[Print[old = r = 2]; Sow[old]; For[n = 2, n <= 10^6, n++, d = GCD[old, If[OddQ[n], n-2, n]]; If[d>r, r=d; Print[d]; Sow[d]]; old += d]][[2, 1]] (* _Jean-François Alcover_, Nov 03 2018, from PARI *)
%o (PARI) print1(old=r=2); for(n=2,1e11, d=gcd(old,if(n%2,n-2,n)); if(d>r, r=d; print1(", "d)); old+=d) \\ _Charles R Greathouse IV_, Oct 13 2017
%Y Cf. A166944, A084662, A084663, A106108, A132199, A134162, A135506, A135508, A118679, A120293.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Oct 24 2009, Nov 05 2009
%E 6 more terms from _R. J. Mathar_, Nov 19 2009; extension beginning with a(19) from _Benoit Cloitre_ (private communication to Vladimir Shevelev)
%E a(25), a(26) from _D. S. McNeil_, Dec 13 2010
%E a(27)-a(30) from _Charles R Greathouse IV_, Oct 13 2017
%E a(31)-a(35) from _Charles R Greathouse IV_, Oct 17 2017
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