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A186267 Generating prime triples. a(n) = b_f(n) where f is the 3-periodic 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 (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..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(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

KEYWORD

nonn,more

AUTHOR

Benoit Cloitre, Feb 16 2011

STATUS

approved

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Last modified July 10 02:05 EDT 2020. Contains 335570 sequences. (Running on oeis4.)