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A186255 a(n) = 3*b_3(n)+2, where b_3 lists the zeros of the sequence A261303: u(n+1)=abs(u(n)-gcd(u(n),3*n+2)), u(1)=1.

%I A186255 #16 Jan 12 2016 10:34:02
%S A186255 8,17,71,269,1013,4007,15923,63521,253949,1014317,4056893,16225589,
%T A186255 64902359,259609439,1038437759,4153750883,16614561281,66458241569,
%U A186255 265832966279,1063331407109,4253325628439,17013302513759,68053207705097,272212800371669,1088851201483883
%N A186255 a(n) = 3*b_3(n)+2, where b_3 lists the zeros of the sequence A261303: u(n+1)=abs(u(n)-gcd(u(n),3*n+2)), u(1)=1.
%C A186255 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=3 it appears a(n) is prime for n>=2.
%C A186255 See A261303 for the sequence u relevant here (m=3). - _M. F. Hasler_, Aug 14 2015
%H A186255 B. Cloitre, <a href="http://arxiv.org/abs/1101.4274">10 conjectures in additive number theory</a>, preprint arxiv:2011.4274
%H A186255 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 A186255 We conjecture that a(n) is asymptotic to c*4^n with c=0.96...
%F A186255 See the wiki link for a sketch of a proof that this is true. We can give more decimals of c = 0.967094... - _M. F. Hasler_, Aug 22 2015
%o A186255 (PARI) a=1; m=3; for(n=2, 10^7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))
%o A186255 (PARI) m=3; a=k=1; for(n=1, 25, 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 A186255 Cf. A106108.
%Y A186255 Cf. A261301 - A261310; A186253 - A186263.
%K A186255 nonn
%O A186255 1,1
%A A186255 _Benoit Cloitre_, Feb 16 2011
%E A186255 More terms from _M. F. Hasler_, Aug 22 2015