

A186265


a(n) = b_f(n) where f is the 2periodic sequence f(k) = (1)^k.


1



2, 5, 11, 23, 41, 61, 107, 197, 311, 617, 1229, 2381, 4649, 8861, 17027, 33809, 67409, 134681, 267719, 535349, 1069217, 2138399, 4275641, 8545697, 17091377, 34182749, 68365469, 136730639, 273461159
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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 for f(k)=(1)^k it appears a(n) and a(n)+2 are twin primes for n>=7. If we start with u(1) large enough (such as with u(1)=71) the sequence will produce only twin primes.


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) a=1; for(n=2, 10^9, t=a; a=abs(agcd(a, n+(1)^n)); if(a==0, print1(n, ", ")))


CROSSREFS

Cf. A186267.
Sequence in context: A039693 A294938 A062475 * A225947 A330909 A281969
Adjacent sequences: A186262 A186263 A186264 * A186266 A186267 A186268


KEYWORD

nonn,more


AUTHOR

Benoit Cloitre, Feb 16 2011


STATUS

approved



