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A168382
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Least number k having n distinct representations as the sum of a nonzero Fibonacci number and a prime.
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2
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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
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1,1
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COMMENTS
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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]
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REFERENCES
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J. Earls, "Fibonacci Prime Decompositions," Mathematical Bliss, Pleroma Publications, 2009, pages 76-79. ASIN: B002ACVZ6O
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LINKS
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Table of n, a(n) for n=1..20.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A132144, A169790, A169791.
Sequence in context: A204521 A073313 A217248 * A155701 A353950 A119529
Adjacent sequences: A168379 A168380 A168381 * A168383 A168384 A168385
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KEYWORD
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more,nonn
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AUTHOR
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Jason Earls, Nov 24 2009
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EXTENSIONS
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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
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STATUS
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approved
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