A153892 - OEIS

%I #41 Mar 08 2024 11:57:50

%S 7,19,31,131,1453,2351,42187,1981891,3206767,13584083,332484016063,

%T 66165989928299,146028309791690867,1619478772188347101,

%U 47020662244482792763,229030451631542624193448579,1569798068858809572115420691

%N Primes that are the sum of five consecutive Fibonacci numbers.

%C 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

%C 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

%C a(29) has 948 digits; a(30) has 1253 digits. - _Harvey P. Dale_, Jan 13 2013

%H Harvey P. Dale, <a href="/A153892/b153892.txt">Table of n, a(n) for n = 1..29</a>

%H Hsin-Yun Ching, Rigoberto Flórez, F. Luca, Antara Mukherjee, and J. C. Saunders, <a href="https://arxiv.org/abs/2211.10788">Primes and composites in the determinant Hosoya triangle</a>, arXiv:2211.10788 [math.NT], 2022.

%H Hsin-Yun Ching, Rigoberto Flórez, F. Luca, Antara Mukherjee, and J. C. Saunders, <a href="https://www.fq.math.ca/Papers1/60-5/ching.pdf">Primes and composites in the determinant Hosoya triangle</a>, The Fibonacci Quarterly, 60.5 (2022), 56-110.

%e a(1) =  7 = 0+1+1+2+3 is prime;

%e a(2) = 19 = 1+2+3+5+8 is prime;

%e a(3) = 31 = 2+3+5+8+13 is prime, etc.

%t Select[Total/@Partition[Fibonacci[Range[0,150]],5,1],PrimeQ] (* _Harvey P. Dale_, Jan 13 2013 *)

%Y Cf. A000045, A001906, A000071, A001605, A013655, A153862, A153863, A153865, A153866, A153867, A153887, A153888, A153889, A153890, A153891.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 03 2009