A167494 List of first differences of A167493 that are different from 1.

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, 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, 3, 17, 3, 113

Offset: 1

Author

Vladimir Shevelev, Nov 05 2009

Keywords

• nonn

Comments

Conjecture. All terms of the sequence are primes.

The conjecture is false: a(144)=27, a(146)=25, a(158)=45, etc., which are composite numbers. - Harvey P. Dale, Dec 05 2015

Links

• Michel Marcus, Table of n, a(n) for n = 1..211
• E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.8.
• 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. [From _Vladimir Shevelev_, Dec 03 2009]

Crossrefs

Cf. A167493, A167197, A167195, A167170, A167168, A106108, A132199, A167054, A167053, A166944, A166945, A116533, A163961, A163963, A084662, A084663, A134162, A135506, A135508, A118679, A120293.

Programs

Mathematica

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 *)

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