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 A186253 Indices of zeros of the sequence u(n)=abs(u(n-1)-gcd(u(n-1),n-1)), u(1)=1. 21
 2, 5, 11, 23, 47, 79, 157, 313, 619, 1237, 2473, 4909, 9817, 19603, 39199, 78193, 156019, 311347, 622669, 1244149, 2487739, 4975111, 9950221, 19900399, 39800797, 79601461, 159202369, 318404629, 636788881, 1273577761, 2547155419, 5094310069, 10188620041 (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=1 it appears a(n) is prime for n>=1. See A261301 for the sequence u relevant here (m=1). - M. F. Hasler, Aug 14 2015 A261301(a(n)-1) = 1; A261301(a(n)) = 0; A261301(a(n)+1) = a(n). - Reinhard Zumkeller, Sep 07 2015 LINKS Moritz Firsching, Table of n, a(n) for n = 1..315 B. Cloitre, 10 conjectures in additive number theory, arXiv:1101.4274 [math.NT], 2011. M. F. Hasler, Rowland-Cloître type prime generating sequences, OEIS Wiki, August 2015. FORMULA Conjecture: a(n) is asymptotic to c*2^n with c = 1.1861... MATHEMATICA a = m = 1; Reap[For[n = 2, n <= 10^7, n++, a = Abs[a - GCD[a, m*n - 1]]; If[a == 0, Print[m*n + m - 1]; Sow[m*n + m - 1]]]][[2, 1]] (* Jean-François Alcover, Feb 05 2019, from PARI *) nxt[{n_, a_}]:={n+1, Abs[a-GCD[a, n]]}; Position[NestList[nxt, {1, 1}, 13*10^5][[All, 2]], 0]// Flatten (* The program generates the first 20 terms of the sequence. *) (* Harvey P. Dale, Oct 02 2022 *) PROG (PARI) a=1; m=1; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", "))) (PARI) next_a(last_a) = { local(A=last_a, B=last_a, C=2*last_a+1); while(A>0, D=divisors(C); k1=10*D[2]; for(j=2, #D, d=D[j]; k=((A+1-B+d)/2)%d; if(k==0, k=d); if(k<=k1, k1=k; d1=d)); if(k1-1+d1==A, B=B+1); A = max(A-(k1-1)-d1, 0); B = B + k1; C = C - (d1 - 1); ); return(B); } a=2 for(n=1, 99, print1(a, ", "); a=next_a(a)) \\ Jan Büthe and Moritz Firsching, Aug 04 2015 (PARI) m=a=k=1; for(n=1, 30, 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 (Haskell) a186253 n = a186253_list !! (n-1) a186253_list = filter ((== 0) . a261301) [1..] -- Reinhard Zumkeller, Sep 07 2015 CROSSREFS Cf. A106108. Cf. A261301 - A261310; A186254 - A186263. Sequence in context: A347309 A174162 A340799 * A226462 A000100 A293339 Adjacent sequences: A186250 A186251 A186252 * A186254 A186255 A186256 KEYWORD nonn AUTHOR Benoit Cloitre, Feb 16 2011 EXTENSIONS Definition clarified by M. F. Hasler, Aug 14 2015 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)