A186260 a(n) = 8*b_8(n)+7, where b_8 lists the zeros of the sequence A261308: u(n+1)=|u(n)-gcd(u(n), 8n+7)|, u(1)=1.

23, 167, 1511, 13463, 120167, 1076039, 9684359, 87158999, 784430279, 7059870119, 63537744791, 571838662007, 5146547952983, 46318929479831, 416870365318487, 3751833287866247, 33766499550040823, 303898495950141767, 2735086463015669687, 24615778167141027047

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=8 it appears a(n) is prime for n>=1.

See A261308 for the sequence u relevant here (m=8). - 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=8; for(n=2, 10^8, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))

PARI

m=8; 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*9^n with c>0.

See the wiki link for a sketch of a proof of this conjecture. We find c = 2.024712577430180... - M. F. Hasler, Aug 22 2015

Extensions

Edited by M. F. Hasler, Aug 14 2015

More terms from M. F. Hasler, Aug 14 2015