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 A113188 Primes that are the difference of two Fibonacci numbers; primes in A007298. 12
 2, 3, 5, 7, 11, 13, 19, 29, 31, 47, 53, 89, 131, 139, 199, 233, 521, 607, 953, 1453, 1597, 2207, 2351, 2579, 3571, 6763, 9349, 10891, 28513, 28649, 28657, 42187, 44771, 46279, 75017, 189653, 317777, 514229, 1981891, 2177699, 3010349, 3206767 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The difference F(i)-F(j) equals the sum F(j-1)+...+F(i-2) [Corrected by Patrick Capelle, Mar 01 2008]. In general, we need gcd(i,j)=1 for F(i)-F(j) to be prime. The exceptions are handled by the following rule: if i and j are both even or both odd, then F(i)-F(j) is prime if either (1) i-j=4 and L(i-2) is a Lucas prime or (2) i-j=2 and F(i-1) is a Fibonacci prime. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 EXAMPLE The prime 139 is here because it is F(12)-F(5). MATHEMATICA lst={}; Do[p=Fibonacci[n]-Fibonacci[i]; If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 40}, {i, n-1}]; Union[lst] PROG (PARI) list(lim)=my(v=List(), F=vector(A130233(lim), i, fibonacci(i)), s, t); for(i=1, #F, s=0; forstep(j=i, 1, -1, s+=F[j]; if(s>lim, break); if(isprime(s), listput(v, s)))); Set(v) \\ Charles R Greathouse IV, Oct 07 2016 CROSSREFS Cf. A000045 (Fibonacci numbers), A001605 (Fibonacci(n) is prime), A001606 (Lucas(n) is prime), A113189 (number of times that Fibonacci(n)-Fibonacci(i) is prime for i=0..n-3). Sequence in context: A155108 A356856 A222565 * A358718 A242738 A079153 Adjacent sequences: A113185 A113186 A113187 * A113189 A113190 A113191 KEYWORD nonn AUTHOR T. D. Noe, Oct 17 2005 STATUS approved

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Last modified March 31 06:13 EDT 2023. Contains 361634 sequences. (Running on oeis4.)