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 A186259 a(n) = 7*b_7(n) + 6, where b_7 lists the indices of zeros of the sequence u(n) = abs(u(n-1) - gcd(u(n-1), 7n-1)), u(1) = 1. 1
 20, 167, 797, 6299, 48817, 389437, 3114313, 24910031, 199280101, 1594149787, 12752862247, 102022886167, 816183074713, 6529464593329, 52235716720753, 417885733765933, 3343085868722137, 26744686949777089, 213957495598165381, 1711659964119801373 (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=7 it appears a(n) is prime for n>=2. See A261307 for the sequence u relevant here (m=7). - 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*8^n with c>0. See the wiki link for a sketch of a proof of this conjecture. We find c = 1.48462836... - M. F. Hasler, Aug 22 2015 PROG (PARI) a=1; m=7; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", "))) (PARI) m=7; 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: A289181 A056114 A281204 * A292281 A056932 A304508 Adjacent sequences:  A186256 A186257 A186258 * A186260 A186261 A186262 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 March 19 13:29 EDT 2019. Contains 321330 sequences. (Running on oeis4.)