

A186260


a(n) = 8*b_8(n)+7, where b_8 lists the zeros of the sequence A261308: u(n+1)=u(n)gcd(u(n), 8n+7), u(1)=1.


1



23, 167, 1511, 13463, 120167, 1076039, 9684359, 87158999, 784430279, 7059870119, 63537744791, 571838662007, 5146547952983, 46318929479831, 416870365318487, 3751833287866247, 33766499550040823, 303898495950141767, 2735086463015669687, 24615778167141027047
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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=8 it appears a(n) is prime for n>=1.
See A261308 for the sequence u relevant here (m=8).  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*9^n with c>0.
See the wiki link for a sketch of a proof of this conjecture. We find c = 2.024712577430180...  M. F. Hasler, Aug 22 2015


PROG

(PARI) a=1; m=8; for(n=2, 10^8, a=abs(agcd(a, m*n1)); if(a==0, print1(m*n+m1, ", ")))
(PARI) m=8; a=k=1; for(n=1, 20, 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: A168027 A155842 A248698 * A229426 A274587 A302200
Adjacent sequences: A186257 A186258 A186259 * A186261 A186262 A186263


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Feb 16 2011


EXTENSIONS

Edited by M. F. Hasler, Aug 14 2015
More terms from M. F. Hasler, Aug 14 2015


STATUS

approved



