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%I #14 Jan 12 2016 10:35:19
%S 11,59,251,1259,6299,31387,152083,758971,3790651,18953251,94766251,
%T 473831251,2369156107,11845755043,59228775043,296143874947,
%U 1480718773123,7403593861843,37017965808931,185089757395379,925448786976163,4627243883546971,23136219387534283
%N a(n) = 4*b_4(n)+3, where b_4 lists the indices of zeros of the sequence A261304: u(n) = abs(u(n-1)-gcd(u(n-1),4*n-1)), 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=4 it appears a(n) is prime for n>=1.
%C See A261304 for the sequence u relevant here (m=4). - _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*5^n with c=1.9408...
%F See the wiki link for a sketch of a proof of this conjecture. We can give more decimals of c = 1.94080675... - _M. F. Hasler_, Aug 22 2015
%o (PARI) a=1; m=4; for(n=2, 1e7,a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))
%o (PARI) m=4; 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 Cf. A106108.
%Y Cf. A261301 - A261310; A186253 - A186263.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Feb 16 2011
%E More terms from _M. F. Hasler_, Aug 22 2015
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