A186258 a(n) = 6*b_6(n)+5, where b_6 lists the indices of zeros of the sequence A261306: u(n) = abs(u(n-1)-gcd(u(n-1),6*n-1)), u(1) = 1.

17, 101, 461, 2801, 19553, 136649, 955841, 6684749, 46777229, 327440609, 2292083093, 16044575777, 112312028681, 786179138273, 5503253967269, 38522774910593, 269659405576049, 1887615818410877, 13213310659503893, 92493174561607361

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=6 it appears a(n) is prime for n>=1.

See A261306 for the sequence u relevant here (m=6). - 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=6; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))

PARI

m=6; a=k=1; for(n=1, 20, 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*7^n with c>0.

See the wiki link for a sketch of a proof of this conjecture. We find c = 1.15917467758687... - M. F. Hasler, Aug 22 2015

Extensions

Edited by M. F. Hasler, Aug 14 2015

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