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 A186259 #10 Jan 12 2016 10:40:50
%S A186259 20,167,797,6299,48817,389437,3114313,24910031,199280101,1594149787,
%T A186259 12752862247,102022886167,816183074713,6529464593329,52235716720753,
%U A186259 417885733765933,3343085868722137,26744686949777089,213957495598165381,1711659964119801373
%N A186259 a(n) = 7*b_7(n) + 6, where b_7 lists the indices of zeros of the sequence u(n) = abs(u(n-1) - gcd(u(n-1), 7n-1)), u(1) = 1.
%C A186259 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=7 it appears a(n) is prime for n>=2.
%C A186259 See A261307 for the sequence u relevant here (m=7). - _M. F. Hasler_, Aug 14 2015
%H A186259 B. Cloitre, <a href="http://arxiv.org/abs/1101.4274">10 conjectures in additive number theory</a>, preprint arxiv:2011.4274 (2011).
%H A186259 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 A186259 We conjecture that a(n) is asymptotic to c*8^n with c>0.
%F A186259 See the wiki link for a sketch of a proof of this conjecture. We find c = 1.48462836... - _M. F. Hasler_, Aug 22 2015
%o A186259 (PARI) a=1; m=7; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))
%o A186259 (PARI) m=7; 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 A186259 Cf. A106108.
%Y A186259 Cf. A261301 - A261310; A186253 - A186263.
%K A186259 nonn
%O A186259 1,1
%A A186259 _Benoit Cloitre_, Feb 16 2011
%E A186259 Edited by _M. F. Hasler_, Aug 14 2015
%E A186259 More terms from _M. F. Hasler_, Aug 22 2015