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 A186263 a(n) = 10*b_10(n) + 9, where b_10 lists the indices of zeros of the sequence A261310: u(n) = abs(u(n-1) - gcd(u(n-1), 10n-1)), u(1) = 1. 19
 29, 269, 2969, 32609, 357169, 3928669, 43213789, 475113649, 5226205969, 57488152069, 632360271769, 6955957188049, 76515529068529, 841670819753809, 9258379017291889, 101842168949117209, 1120263858440288929, 12322902442843176229, 135551926871245562989 (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=10 it appears a(n) is prime for n>=1. See A261310 for the sequence u relevant here (m=10). - 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*11^n with c>0. See the wiki link for a sketch of a proof of this conjecture. We find c = 2.2163823215... - M. F. Hasler, Aug 22 2015 PROG PARI) a=1; m=10; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", "))) (PARI) m=10; 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 - A186261. Sequence in context: A223776 A224408 A120823 * A110692 A081684 A142033 Adjacent sequences:  A186260 A186261 A186262 * A186264 A186265 A186266 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 June 21 03:51 EDT 2021. Contains 345354 sequences. (Running on oeis4.)