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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
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
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
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