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

1,1

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=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

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*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

Prog

(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

Crossrefs

Cf. A106108.

Cf. A261301 - A261310; A186253 - A186263.

Sequence in context: A168027 A155842 A248698 * A229426 A274587 A302200

Adjacent sequences: A186257 A186258 A186259 * A186261 A186262 A186263

Keyword

nonn

Author

Benoit Cloitre, Feb 16 2011

Extensions

Edited by M. F. Hasler, Aug 14 2015

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

Status

approved