This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A186263 #21 May 12 2023 01:34:11
%S A186263 29,269,2969,32609,357169,3928669,43213789,475113649,5226205969,
%T A186263 57488152069,632360271769,6955957188049,76515529068529,
%U A186263 841670819753809,9258379017291889,101842168949117209,1120263858440288929,12322902442843176229,135551926871245562989
%N A186263 a(n) = 10*b_10(n) + 9, where b_10 lists the indices of zeros of the sequence A261310: u(n) = abs(u(n-1) - gcd(u(n-1), 10n-1)), u(1) = 1.
%C A186263 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=10 it appears a(n) is prime for n>=1.
%C A186263 See A261310 for the sequence u relevant here (m=10). - _M. F. Hasler_, Aug 14 2015
%H A186263 Benoit Cloitre, <a href="http://arxiv.org/abs/1101.4274">10 conjectures in additive number theory</a>, preprint arXiv:2011.4274 [math.NT] , 2011.
%H A186263 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 A186263 We conjecture that a(n) is asymptotic to c*11^n with c>0.
%F A186263 See the wiki link for a sketch of a proof of this conjecture. We find c = 2.2163823215... - _M. F. Hasler_, Aug 22 2015
%o A186263 (PARI) a=1; m=10; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))
%o A186263 (PARI) m=10; 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 A186263 Cf. A106108.
%Y A186263 Cf. A261301 - A261310; A186253 - A186261.
%K A186263 nonn
%O A186263 1,1
%A A186263 _Benoit Cloitre_, Feb 16 2011
%E A186263 Edited by _M. F. Hasler_, Aug 14 2015
%E A186263 More terms from _M. F. Hasler_, Aug 22 2015