A186256 a(n) = 4*b_4(n)+3, where b_4 lists the indices of zeros of the sequence A261304: u(n) = abs(u(n-1)-gcd(u(n-1),4*n-1)), u(1) = 1.

11, 59, 251, 1259, 6299, 31387, 152083, 758971, 3790651, 18953251, 94766251, 473831251, 2369156107, 11845755043, 59228775043, 296143874947, 1480718773123, 7403593861843, 37017965808931, 185089757395379, 925448786976163, 4627243883546971, 23136219387534283

Offset: 1

Author

Benoit Cloitre, Feb 16 2011

Keywords

• nonn

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=4 it appears a(n) is prime for n>=1.

See A261304 for the sequence u relevant here (m=4). - M. F. Hasler, Aug 14 2015

Links

• B. Cloitre, 10 conjectures in additive number theory, preprint arxiv:2011.4274 (2011).
• M. F. Hasler, Rowland-Cloître type prime generating sequences, OEIS Wiki, August 2015.

Crossrefs

Cf. A106108.

Cf. A261301 - A261310; A186253 - A186263.

Programs

PARI

a=1; m=4; for(n=2, 1e7,a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))

PARI

m=4; a=k=1; for(n=1, 25, 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

Formula

We conjecture that a(n) is asymptotic to c*5^n with c=1.9408...

See the wiki link for a sketch of a proof of this conjecture. We can give more decimals of c = 1.94080675... - M. F. Hasler, Aug 22 2015

Extensions

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