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, a=abs(a-gcd(a, n+(-1)^n)); if(a==0, print1(n, ", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 16 2011
EXTENSIONS
More terms from Jinyuan Wang, Jan 09 2021
STATUS
approved