A169791 Least number k having n distinct representations as the sum of a nonzero Fibonacci number and a prime.

9, 3, 4, 8, 24, 74, 444, 1614, 15684, 29400, 50124, 556274, 5332128, 11110428, 50395440, 509562294, 1296895890, 13314115434, 187660997904, 326585290794, 4788143252148

Offset: 1

Author

R. J. Mathar and Jon E. Schoenfield, May 14 2010

Keywords

• nonn
• more

Comments

We count ordered index pairs (i,j) that represent k = Fibonacci(i) + prime(j), i >= 1, j >= 1.

A variant of A168382, because Fibonacci(1)=1 and Fibonacci(2)=1 may both contribute individually to the count.

Fibonacci(1) + prime(4) = Fibonacci(2) + prime(4) = Fibonacci(4) + prime(3) = Fibonacci(5) + prime(2) = 8 are four "distinct" representations of k=8, because Fibonacci(1) = Fibonacci(2) are treated as distinguishable.

a(18) > 10^10. [Donovan Johnson, May 17 2010]

Except for a(1), all terms appear to be of the form p+1 for some prime p. - Chai Wah Wu, Dec 06 2019

Examples

			1+443 = 1+443 = 5+439 = 13+431 = 55+389 = 233+211 = 377+67 are n=7 distinct representations of k=444.
		

Crossrefs

Cf. A168382, A169790.

Extensions

a(12)-a(15) from Max Alekseyev, May 15 2010

a(16)-a(17) from Donovan Johnson, May 17 2010

A prime index in the comment corrected by R. J. Mathar, Jun 02 2010

a(18) from Chai Wah Wu, Dec 06 2019

a(19)-a(21) from Giovanni Resta, Dec 10 2019