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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...

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: A192580 A075712 A174162 * A226462 A000100 A175867

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 June 28 04:43 EDT 2017. Contains 288813 sequences.