

A186257


a(n) = 5*b_5(n)+4, where b_5 lists the indices of zeros of the sequence A261305: u(n) = abs(u(n1)gcd(u(n1),5*n1)), u(1) = 1.


0



14, 89, 479, 2879, 17099, 99839, 599009, 3592859, 21557099, 129336149, 775914479, 4655486369, 27932918219, 167597509319, 1005582321329, 6033492323549, 36200953941059, 217205705087639, 1303234230378959, 7819405361540219
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OFFSET

1,1


COMMENTS

For any fixed integer m>=1 define u(1)=1 and u(n)=abs(u(n1)gcd(u(n1),m*n1)). 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)+m1 is a prime number. Here for m=5 it appears a(n) is prime for n>=2.
See A261305 for the sequence u relevant here (m=5).  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, RowlandCloĆ®tre type prime generating sequences, OEIS Wiki, August 2015.


FORMULA

We conjecture that a(n) is asymptotic to c*6^n with c>0.
See the wiki link for a sketch of a proof of this conjecture. More precisely we find c = 1.15917467761...  M. F. Hasler, Aug 22 2015


PROG

(PARI) a=1; m=5; for(n=2, 1e7, a=abs(agcd(a, m*n1)); if(a==0, print1(m*n+m1, ", ")))
(PARI) m=5; a=k=1; for(n=1, 25, while( a>D=vecmin(apply(p>a%p, factor(N=m*(k+a)+m1)[, 1])), a=D+gcd(aD, 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: A255535 A034544 A248060 * A241305 A195267 A077538
Adjacent sequences: A186254 A186255 A186256 * A186258 A186259 A186260


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



