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 A260222 a(n)=gcd(n,F(n-1)), where F(n) is the n-th Fibonacci number. 2
 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 11, 1, 1, 1, 1, 2, 1, 1, 19, 1, 3, 2, 1, 1, 1, 1, 1, 2, 29, 1, 31, 1, 3, 2, 1, 1, 1, 1, 1, 2, 41, 1, 1, 1, 3, 2, 1, 1, 7, 1, 1, 2, 1, 1, 1, 1, 3, 2, 59, 1, 61, 1, 1, 2, 1, 1, 1, 1, 3, 2, 71, 1, 1, 1, 1, 2, 1, 13, 79, 1, 3, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS This sequence seems good at generating primes, in particular, twin primes. Many primes p are generated when a(p)=p. In fact for n<=10000, a(n)=n occurs 617 times and 609 of these times n is prime. Furthermore, 275 of these times n is also a twin prime. For n<=1000000 and a(n)=n this sequence generates 39210 primes (49.95% of primes in the range) and produces a prime 99.75% of the time. At the same time it generates 10864 twin primes, which is 66.50% of all twin primes in the range. A260228 is a similar sequence that produces more primes. It is well known that p|F(p-(p/5)) for every prime p. So a(p) = p for any prime p == 1,4 (mod 5). - Zhi-Wei Sun, Aug 29, 2015 LINKS Dmitry Kamenetsky, Table of n, a(n) for n = 1..10000 Z.-H. Sun and Z.-W. Sun, Fibonacci numbers and Fermat's last theorem, Acta Arithmetica 60(4) (1992), 371-388. EXAMPLE a(2) = gcd(2,F(1)) = gcd(2,1) = 1. a(11) = gcd(11,F(10)) = gcd(11,55) = 11. a(19) = gcd(19,2584) = 19. a(29) = gcd(29,317811) = 29. MATHEMATICA Table[GCD[n, Fibonacci[n-1]], {n, 1, 80}] (* Vincenzo Librandi, Jul 20 2015 *) PROG (PARI) a(n)=gcd(n, fibonacci(n-1)) first(m)=vector(m, n, a(n+1)) /* Anders Hellström, Jul 19 2015 */ (MAGMA) [Gcd(n, Fibonacci(n-1)): n in [1..90]]; // Vincenzo Librandi, Jul 20 2015 CROSSREFS Cf. A104714, A106108, A260228. Sequence in context: A026536 A046213 A215625 * A181386 A193517 A296554 Adjacent sequences:  A260219 A260220 A260221 * A260223 A260224 A260225 KEYWORD nonn AUTHOR Dmitry Kamenetsky, Jul 19 2015 STATUS approved

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Last modified May 10 02:36 EDT 2021. Contains 343747 sequences. (Running on oeis4.)