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 A186260 a(n) = 8*b_8(n)+7, where b_8 lists the zeros of the sequence A261308: u(n+1)=|u(n)-gcd(u(n), 8n+7)|, u(1)=1. 1
 23, 167, 1511, 13463, 120167, 1076039, 9684359, 87158999, 784430279, 7059870119, 63537744791, 571838662007, 5146547952983, 46318929479831, 416870365318487, 3751833287866247, 33766499550040823, 303898495950141767, 2735086463015669687, 24615778167141027047 (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=8 it appears a(n) is prime for n>=1. See A261308 for the sequence u relevant here (m=8). - 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*9^n with c>0. See the wiki link for a sketch of a proof of this conjecture. We find c = 2.024712577430180... - M. F. Hasler, Aug 22 2015 PROG (PARI) a=1; m=8; for(n=2, 10^8, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", "))) (PARI) m=8; 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: A168027 A155842 A248698 * A229426 A274587 A302200 Adjacent sequences:  A186257 A186258 A186259 * A186261 A186262 A186263 KEYWORD nonn AUTHOR Benoit Cloitre, Feb 16 2011 EXTENSIONS Edited by M. F. Hasler, Aug 14 2015 More terms from M. F. Hasler, Aug 14 2015 STATUS approved

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Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)