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A168382 Least number k having n distinct representations as the sum of a nonzero Fibonacci number and a prime. 2

%I #19 Dec 11 2019 02:34:00

%S 3,4,8,24,74,444,1600,15684,29400,50124,259224,5332128,11110428,

%T 50395440,451174728,1296895890,13314115434,32868437466,326585290794,

%U 4788143252148

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

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

%C 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.

%C a(17) > 10^10. [_Donovan Johnson_, May 17 2010]

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

%e 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.

%Y Cf. A132144, A169790, A169791.

%K more,nonn

%O 1,1

%A _Jason Earls_, Nov 24 2009

%E Two more terms from _R. J. Mathar_, Feb 07 2010

%E a(7) corrected by _Jon E. Schoenfield_, May 14 2010

%E Edited by _R. J. Mathar_, May 14 2010

%E a(11)-a(14) from _Max Alekseyev_, May 15 2010

%E a(15)-a(16) from _Donovan Johnson_, May 17 2010

%E a(17) from _Chai Wah Wu_, Sep 04 2018

%E a(18)-a(20) from _Giovanni Resta_, Dec 10 2019

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)