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

1,1

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]

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A138663 A330834 A056149 * A091238 A178047 A122954

Adjacent sequences: A167491 A167492 A167493 * A167495 A167496 A167497

Keyword

nonn

Author

Vladimir Shevelev, Nov 05 2009

Status

approved