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.

20, 167, 797, 6299, 48817, 389437, 3114313, 24910031, 199280101, 1594149787, 12752862247, 102022886167, 816183074713, 6529464593329, 52235716720753, 417885733765933, 3343085868722137, 26744686949777089, 213957495598165381, 1711659964119801373

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

Table of n, a(n) for n=1..20.

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*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