|
%I #25 Dec 13 2018 19:06:04
%S 2,3,3,5,3,13,5,3,31,61,7,5,3,7,139,5,3,283,5,3,571,7,5,3,1153,5,3,
%T 2311,31,4651,17,5,13,3,3,5,3,9343,5,3,11,3,59,3,29,3,19,7,5,3,7,19,5,
%U 3,17,3,113
%N List of first differences of A167493 that are different from 1.
%C Conjecture. All terms of the sequence are primes.
%C The conjecture is false: a(144)=27, a(146)=25, a(158)=45, etc., which are composite numbers. - _Harvey P. Dale_, Dec 05 2015
%H Michel Marcus, <a href="/A167494/b167494.txt">Table of n, a(n) for n = 1..211</a>
%H E. S. Rowland, <a href="http://www.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.
%H V. Shevelev, <a href="http://arxiv.org/abs/0910.4676">A new generator of primes based on the Rowland idea</a>, arXiv:0910.4676 [math.NT], 2009.
%H V. Shevelev, <a href="http://arxiv.org/abs/0911.5478">Three theorems on twin primes</a>, arXiv:0911.5478 [math.NT], 2009-2010. [From _Vladimir Shevelev_, Dec 03 2009]
%t nxt[{n_,a_}]:={n+1,If[EvenQ[n],a+GCD[n+1,a],a+GCD[n-1,a]]}; DeleteCases[ Differences[ Transpose[NestList[nxt,{1,2},20000]][[2]]],1] (* _Harvey P. Dale_, Dec 05 2015 *)
%o (PARI) lista(nn) = {my(va = vector(nn)); va[1] = 2; for (n=2, nn, va[n] = if (n%2, va[n-1] + gcd(n, va[n-1]), va[n-1] + gcd(n-2, va[n-1]));); select(x->(x!=1), vector(nn-1, n, va[n+1] - va[n]));} \\ _Michel Marcus_, Dec 13 2018
%Y Cf. A167493, A167197, A167195, A167170, A167168, A106108, A132199, A167054, A167053, A166944, A166945, A116533, A163961, A163963, A084662, A084663, A134162, A135506, A135508, A118679, A120293.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Nov 05 2009
|
