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 A186257 a(n) = 5*b_5(n)+4, where b_5 lists the indices of zeros of the sequence A261305: u(n) = abs(u(n-1)-gcd(u(n-1),5*n-1)), u(1) = 1. 0
 14, 89, 479, 2879, 17099, 99839, 599009, 3592859, 21557099, 129336149, 775914479, 4655486369, 27932918219, 167597509319, 1005582321329, 6033492323549, 36200953941059, 217205705087639, 1303234230378959, 7819405361540219 (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=5 it appears a(n) is prime for n>=2. See A261305 for the sequence u relevant here (m=5). - M. F. Hasler, Aug 14 2015 LINKS B. Cloitre, 10 conjectures in additive number theory, preprint arxiv:2011.4274 (2011). M. F. Hasler, Rowland-CloĆ®tre type prime generating sequences, OEIS Wiki, August 2015. FORMULA We conjecture that a(n) is asymptotic to c*6^n with c>0. See the wiki link for a sketch of a proof of this conjecture. More precisely we find c = 1.15917467761... - M. F. Hasler, Aug 22 2015 PROG (PARI) a=1; m=5; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", "))) (PARI) m=5; 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 CROSSREFS Cf. A106108. Cf. A261301 - A261310; A186253 - A186263. Sequence in context: A255535 A034544 A248060 * A241305 A195267 A077538 Adjacent sequences:  A186254 A186255 A186256 * A186258 A186259 A186260 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 January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)