A186257 a(n) = 5*b_5(n)+4, where b_5 lists the indices of zeros of the sequence A261305: u(n) = abs(u(n-1)-gcd(u(n-1),5*n-1)), u(1) = 1.

14, 89, 479, 2879, 17099, 99839, 599009, 3592859, 21557099, 129336149, 775914479, 4655486369, 27932918219, 167597509319, 1005582321329, 6033492323549, 36200953941059, 217205705087639, 1303234230378959, 7819405361540219

Offset

1,1

Comments

For any fixed integer m>=1 define u(1)=1 and u(n)=abs(u(n-1)-gcd(u(n-1),m*n-1)). Then (b_m(k))_{k>=1} is the sequence of integers such that u(b_m(k))=0 and we conjecture that for k large enough m*b_m(k)+m-1 is a prime number. Here for m=5 it appears a(n) is prime for n>=2.

See A261305 for the sequence u relevant here (m=5). - M. F. Hasler, Aug 14 2015

Links

Table of n, a(n) for n=1..20.

B. Cloitre, 10 conjectures in additive number theory, preprint arxiv:2011.4274 (2011).

M. F. Hasler, Rowland-Cloître type prime generating sequences, OEIS Wiki, August 2015.

Formula

We conjecture that a(n) is asymptotic to c*6^n with c>0.

See the wiki link for a sketch of a proof of this conjecture. More precisely we find c = 1.15917467761... - M. F. Hasler, Aug 22 2015

Prog

(PARI) a=1; m=5; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))
(PARI) m=5; a=k=1; for(n=1, 25, while( a>D=vecmin(apply(p->a%p, factor(N=m*(k+a)+m-1)[, 1])), a-=D+gcd(a-D, N); k+=1+D); k+=a+1; print1(a=N, ", ")) \\ M. F. Hasler, Aug 22 2015

Crossrefs

Cf. A106108.

Cf. A261301 - A261310; A186253 - A186263.

Sequence in context: A255535 A034544 A248060 * A241305 A195267 A077538

Adjacent sequences: A186254 A186255 A186256 * A186258 A186259 A186260

Keyword

nonn

Author

Benoit Cloitre, Feb 16 2011

Extensions

Edited by M. F. Hasler, Aug 14 2015

More terms from M. F. Hasler, Aug 22 2015

Status

approved