

A168382


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


2



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

1,1


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]


REFERENCES

J. Earls, "Fibonacci Prime Decompositions," Mathematical Bliss, Pleroma Publications, 2009, pages 7679. ASIN: B002ACVZ6O


LINKS

Table of n, a(n) for n=1..20.


EXAMPLE

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.


CROSSREFS

Cf. A132144, A169790, A169791.
Sequence in context: A204521 A073313 A217248 * A155701 A119529 A180629
Adjacent sequences: A168379 A168380 A168381 * A168383 A168384 A168385


KEYWORD

more,nonn


AUTHOR

Jason Earls, Nov 24 2009


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


STATUS

approved



