A186254 a(n) = 2*b(n)+1, where b(n) lists the zeros of the sequence u(n)=abs(u(n-1)-gcd(u(n-1),2*n-1)), u(1)=1.

5, 17, 53, 149, 449, 1289, 3761, 11261, 33773, 101117, 302681, 907757, 2723069, 8169137, 24506597, 73519793, 220559369, 661677761, 1985001917, 5955003077, 17865008333, 53595020201, 160785060361, 482355180761, 1447065541373, 4341196624109, 13023589872329

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 all k large enough, m*b_m(k)+m-1 is a prime number. Here for m=2 it appears a(n) is prime for n>=1.

See A261302 for the sequence u relevant here (m=2). - M. F. Hasler, Aug 14 2015

Links

Table of n, a(n) for n=1..27.

B. Cloitre, 10 conjectures in additive number theory, arXiv:1101.4274 [math.NT], 2011.

M. F. Hasler, Rowland-Cloître type prime generating sequences, OEIS Wiki, August 2015.

Formula

a(n+1) <= 3*a(n)+2 for all n.- See the wiki link for a sketch of a proof that a(n) ~ c*3^n with c = 1.7078779... - M. F. Hasler, Aug 22 2015

Prog

(PARI) a=1; m=2; for(n=2, 9e9, if(!a=abs(a-gcd(a, m*n-1)), print1(m*n+m-1, ", ")))
(PARI) m=2; a=k=1; for(n=1, 30, 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, A186253 - A186263.

Cf. A261301 - A261310.

Sequence in context: A240693 A278464 A349974 * A158896 A294781 A110318

Adjacent sequences: A186251 A186252 A186253 * A186255 A186256 A186257

Keyword

nonn

Author

Benoit Cloitre, Feb 16 2011

Extensions

More terms from M. F. Hasler, Aug 22 2015

Status

approved