OFFSET
1,1
COMMENTS
Primes of the form F(k+3)+L(k+2), where F(k) and L(k) are the k-th Fibonacci number and Lucas number, respectively. This formula also gives that 3,2 and 5 are primes of the form F(k+3)+L(k+2), with k=-2, k=-1, k=0, respectively. - Rigoberto Florez, Jul 31 2022
Are there infinitely many primes of the form F(k+3)+L(k+2)? There are 47 primes of this form for k <= 80000. There are no such primes for 64000 <= k <= 80000. - Rigoberto Florez, Feb 26 2023
a(29) has 948 digits; a(30) has 1253 digits. - Harvey P. Dale, Jan 13 2013
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..29
Hsin-Yun Ching, Rigoberto Flórez, F. Luca, Antara Mukherjee, and J. C. Saunders, Primes and composites in the determinant Hosoya triangle, arXiv:2211.10788 [math.NT], 2022.
Hsin-Yun Ching, Rigoberto Flórez, F. Luca, Antara Mukherjee, and J. C. Saunders, Primes and composites in the determinant Hosoya triangle, The Fibonacci Quarterly, 60.5 (2022), 56-110.
EXAMPLE
a(1) = 7 = 0+1+1+2+3 is prime;
a(2) = 19 = 1+2+3+5+8 is prime;
a(3) = 31 = 2+3+5+8+13 is prime, etc.
MATHEMATICA
Select[Total/@Partition[Fibonacci[Range[0, 150]], 5, 1], PrimeQ] (* Harvey P. Dale, Jan 13 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jan 03 2009
STATUS
approved