A168382 Least number k having n distinct representations as the sum of a nonzero Fibonacci number and a prime.

3, 4, 8, 24, 74, 444, 1600, 15684, 29400, 50124, 259224, 5332128, 11110428, 50395440, 451174728, 1296895890, 13314115434, 32868437466, 326585290794, 4788143252148

Offset: 1

Author

Jason Earls, Nov 24 2009

Keywords

• more
• nonn

Comments

The meaning of "distinct" is the following: we count ordered index pairs (i,j) with k = Fibonacci(i) + prime(j), i > 1, j >= 1.

Fibonacci(1) + prime(4) = Fibonacci(2) + prime(4) = Fibonacci(4) + prime(3) = Fibonacci(5) + prime(2) = 8 are three "distinct" representations of k=8, because Fibonacci(1) = Fibonacci(2) is treated as indistinguishable, whereas Fibonacci(4) = prime(2) are distinguishable based on the ordering in the indices (ordering in the sum): k = 1+7 = 3+5 = 5+3.

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

Examples

			15684 is the least number having eight distinct representations due to the following sums: 1 + 15683 = 5 + 15679 = 13 + 15671 = 55 + 15629 = 233 + 15451 = 377 + 15307 = 1597 + 14087 = 4181 + 11503.
		

References

• J. Earls, "Fibonacci Prime Decompositions," Mathematical Bliss, Pleroma Publications, 2009, pages 76-79. ASIN: B002ACVZ6O

Crossrefs

Cf. A132144, A169790, A169791.

Extensions

Two more terms from R. J. Mathar, Feb 07 2010

a(7) corrected by Jon E. Schoenfield, May 14 2010

Edited by R. J. Mathar, May 14 2010

a(11)-a(14) from Max Alekseyev, May 15 2010

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

a(17) from Chai Wah Wu, Sep 04 2018

a(18)-a(20) from Giovanni Resta, Dec 10 2019