cp's OEIS Frontend

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.

%I A186261 #14 Jan 12 2016 10:49:30
%S A186261 26,269,2699,26423,259829,2595473,25954289,259491059,2594910599,
%T A186261 25949104721,259491047219,2594905133453,25949039883929,
%U A186261 259490398799609,2594903521711517,25949035214699921,259490352146949701,2594903520789157301,25949035207891572929,259490352078915446897
%N 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.
%C A186261 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.
%C A186261 See A261309 for the sequence u relevant here (m=9). - _M. F. Hasler_, Aug 14 2015
%H A186261 B. Cloitre, <a href="http://arxiv.org/abs/1101.4274">10 conjectures in additive number theory</a>, preprint arxiv:2011.4274 (2011).
%H A186261 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 A186261 We conjecture that a(n) is asymptotic to c*10^n with c>0.
%F A186261 See the wiki link for a sketch of a proof of this conjecture. We find c=2.59490352... - _M. F. Hasler_, Aug 22 2015
%o A186261 (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, ", ")))
%o A186261 (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
%Y A186261 Cf. A106108.
%Y A186261 Cf. A261301 - A261310; A186253 - A186263.
%K A186261 nonn
%O A186261 1,1
%A A186261 _Benoit Cloitre_, Feb 16 2011
%E A186261 Edited by _M. F. Hasler_, Aug 14 2015