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

Author

Benoit Cloitre, Feb 16 2011

Keywords

• nonn

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

• 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.

Crossrefs

Cf. A106108.

Cf. A261301 - A261310; A186253 - A186263.

Programs

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

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

Extensions

Edited by M. F. Hasler, Aug 14 2015

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