A169790 Least number k having n unordered partitions into a nonzero Fibonacci number and a prime.

3, 4, 10, 24, 74, 444, 1614, 15684, 29400, 50124, 259224, 5332128, 11110428, 50395440, 451174728, 1296895890

Offset: 1

Author

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

Keywords

• more
• nonn

Comments

Variant of A168382.

Fibonacci(1) + prime(4) = Fibonacci(2) + prime(4) = Fibonacci(4) + prime(3) = Fibonacci(5) + prime(2) = 8 are two "distinct" representations of k=8, because Fibonacci(1) = Fibonacci(2) = 1 is treated as indistinguishable, and Fibonacci(4) = prime(2) = 3 are also indistinguishable: k = 1+7 = 3+5.

This matters because of the existence of Fibonacci primes (see A005478).

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

Examples

			1+443 = 5+439 = 13+431 = 55+389 = 233+211 = 377+67 are n=6 distinct representations of 444.
		

Crossrefs

Cf. A168382, A169791.

Extensions

a(8)-a(14) from Max Alekseyev, May 15 2010

a(15)-a(16) from Donovan Johnson, May 17 2010

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