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 A186265 a(n) = b_f(n) where f is the 2-periodic 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 (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 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 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(a-gcd(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

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)