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.

29, 269, 2969, 32609, 357169, 3928669, 43213789, 475113649, 5226205969, 57488152069, 632360271769, 6955957188049, 76515529068529, 841670819753809, 9258379017291889, 101842168949117209, 1120263858440288929, 12322902442843176229, 135551926871245562989

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

Table of n, a(n) for n=1..19.

Benoit Cloitre, 10 conjectures in additive number theory, preprint arXiv:2011.4274 [math.NT] , 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