|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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 76-79. 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 A353950 A119529
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
|
|
|
|