A153892 Primes that are the sum of five consecutive Fibonacci numbers.

7, 19, 31, 131, 1453, 2351, 42187, 1981891, 3206767, 13584083, 332484016063, 66165989928299, 146028309791690867, 1619478772188347101, 47020662244482792763, 229030451631542624193448579, 1569798068858809572115420691

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

• nonn

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

Examples

			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.
		

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.

Crossrefs

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

Programs

Mathematica

Select[Total/@Partition[Fibonacci[Range[0,150]],5,1],PrimeQ] (* Harvey P. Dale, Jan 13 2013 *)