A186267 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A186267

a(n) = b_f(n) where f is the 3-periodic sequence [-1,1,5] (see comments).

2, 11, 19, 41, 71, 107, 191, 301, 431, 565, 857, 1133, 1325, 2657, 5231, 10457, 19421, 29567, 54497, 105527, 211061, 408431, 802127, 1600217, 3200201, 6393911, 12783497, 25566677, 51095411, 102190391, 204347177, 408693977, 817302527, 1634575487, 3269107991

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Let u(1)=1 and u(n)=abs(u(n-1)-gcd(u(n-1),n+f(n))) where f(n) is a periodic sequence with period [f(1),f(2),...,f(beta)]. Then (b_f(k))_{k>=1} is the sequence of integers such that u(b_f(k))=0. We conjecture that for k large enough b_f(k)+1+f(i) is simultaneously prime for i=1,2,...,beta. Here f is a period 3 sequence with period [-1,1,5]. It appears [a(n),a(n)+2,a(n)+6] is a prime triple for n>=14 (a(n)>=2657).

LINKS

Table of n, a(n) for n=1..35.

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

FORMULA

Conjecture: a(n) is asymptotic to c*2^n with c>0.

PROG

(PARI) f(n)=[-1, 1, 5][(n+2)%3+1]

a=1; for(n=2, 1000000000, t=a; a=abs(a-gcd(a, n+f(n))); if(a==0, print1(n, ", ")))

CROSSREFS

Cf. A186265.

Sequence in context: A154765 A163997 A067931 * A067660 A235472 A217308

Adjacent sequences: A186264 A186265 A186266 * A186268 A186269 A186270