

A186267


Generating prime triples. a(n) = b_f(n) where f is the 3periodic sequence [1,1,5].


1



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
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OFFSET

1,1


COMMENTS

Let u(1)=1 and u(n)=abs(u(n1)gcd(u(n1),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..29.
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(agcd(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


KEYWORD

nonn,more


AUTHOR

Benoit Cloitre, Feb 16 2011


STATUS

approved



