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 A186258 a(n) = 6*b_6(n)+5, where b_6 lists the indices of zeros of the sequence A261306: u(n) = abs(u(n-1)-gcd(u(n-1),6*n-1)), u(1) = 1. 1
 17, 101, 461, 2801, 19553, 136649, 955841, 6684749, 46777229, 327440609, 2292083093, 16044575777, 112312028681, 786179138273, 5503253967269, 38522774910593, 269659405576049, 1887615818410877, 13213310659503893, 92493174561607361 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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=6 it appears a(n) is prime for n>=1. See A261306 for the sequence u relevant here (m=6). - M. F. Hasler, Aug 14 2015 LINKS B. Cloitre, 10 conjectures in additive number theory, preprint arxiv:2011.4274 (2011). M. F. Hasler, Rowland-Cloître type prime generating sequences, OEIS Wiki, August 2015. FORMULA We conjecture that a(n) is asymptotic to c*7^n with c>0. See the wiki link for a sketch of a proof of this conjecture. We find c = 1.15917467758687... - M. F. Hasler, Aug 22 2015 PROG (PARI) a=1; m=6; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", "))) (PARI) m=6; 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 CROSSREFS Cf. A106108. Cf. A261301 - A261310; A186253 - A186263. Sequence in context: A139913 A255417 A344868 * A175518 A215234 A145943 Adjacent sequences:  A186255 A186256 A186257 * A186259 A186260 A186261 KEYWORD nonn AUTHOR Benoit Cloitre, Feb 16 2011 EXTENSIONS Edited by M. F. Hasler, Aug 14 2015 More terms from M. F. Hasler, Aug 22 2015 STATUS approved

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Last modified October 26 06:55 EDT 2021. Contains 348257 sequences. (Running on oeis4.)