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%I #17 Jan 12 2016 10:41:48
%S 23,167,1511,13463,120167,1076039,9684359,87158999,784430279,
%T 7059870119,63537744791,571838662007,5146547952983,46318929479831,
%U 416870365318487,3751833287866247,33766499550040823,303898495950141767,2735086463015669687,24615778167141027047
%N 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.
%C 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.
%C See A261308 for the sequence u relevant here (m=8). - _M. F. Hasler_, Aug 14 2015
%H B. Cloitre, <a href="http://arxiv.org/abs/1101.4274">10 conjectures in additive number theory</a>, preprint arxiv:2011.4274 (2011).
%H M. F. Hasler, <a href="https://oeis.org/wiki/User:M._F._Hasler/Work_in_progress/Rowland-Cloitre_type_prime_generating_sequences">Rowland-Cloître type prime generating sequences</a>, OEIS Wiki, August 2015.
%F We conjecture that a(n) is asymptotic to c*9^n with c>0.
%F See the wiki link for a sketch of a proof of this conjecture. We find c = 2.024712577430180... - _M. F. Hasler_, Aug 22 2015
%o (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, ", ")))
%o (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
%Y Cf. A106108.
%Y Cf. A261301 - A261310; A186253 - A186263.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Feb 16 2011
%E Edited by _M. F. Hasler_, Aug 14 2015
%E More terms from _M. F. Hasler_, Aug 14 2015
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