A186261 a(n) = 9*b_9(n) + 8, where b_9 lists the indices of zeros of the sequence A261309: u(n) = abs(u(n-1) - gcd(u(n-1), 9n-1)), u(1) = 1.

26, 269, 2699, 26423, 259829, 2595473, 25954289, 259491059, 2594910599, 25949104721, 259491047219, 2594905133453, 25949039883929, 259490398799609, 2594903521711517, 25949035214699921, 259490352146949701, 2594903520789157301, 25949035207891572929, 259490352078915446897

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=9 it appears a(n) is prime for n>=2.

See A261309 for the sequence u relevant here (m=9). - 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*10^n with c>0.

See the wiki link for a sketch of a proof of this conjecture. We find c=2.59490352... - M. F. Hasler, Aug 22 2015

Prog

(PARI) a=1; m=9; for(n=2, 1e8, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))
(PARI) m=9; a=0; k=2; for(n=1, 20, while(1<#(f=factor(N=m*(k+a)+m-1)[, 1]) && a, k+=1+D=vecmin(apply(p->a%p, f)); a-=D+gcd(a-D, N)); k+=a+1; print1(a=N, ", ")) \\ M. F. Hasler, Aug 22 2015

Crossrefs

Cf. A106108.

Cf. A261301 - A261310; A186253 - A186263.

Sequence in context: A187695 A328874 A195755 * A006045 A022686 A200555

Adjacent sequences: A186258 A186259 A186260 * A186262 A186263 A186264

Keyword

nonn

Author

Benoit Cloitre, Feb 16 2011

Extensions

Edited by M. F. Hasler, Aug 14 2015

Status

approved