A169790 -id:A169790 - cp's OEIS frontend

A169791 Least number k having n distinct representations as the sum of a nonzero Fibonacci number and a prime.

9, 3, 4, 8, 24, 74, 444, 1614, 15684, 29400, 50124, 556274, 5332128, 11110428, 50395440, 509562294, 1296895890, 13314115434, 187660997904, 326585290794, 4788143252148

Offset: 1

R. J. Mathar and Jon E. Schoenfield, May 14 2010

We count ordered index pairs (i,j) that represent k = Fibonacci(i) + prime(j), i >= 1, j >= 1.
A variant of A168382, because Fibonacci(1)=1 and Fibonacci(2)=1 may both contribute individually to the count.
Fibonacci(1) + prime(4) = Fibonacci(2) + prime(4) = Fibonacci(4) + prime(3) = Fibonacci(5) + prime(2) = 8 are four "distinct" representations of k=8, because Fibonacci(1) = Fibonacci(2) are treated as distinguishable.
a(18) > 10^10. [Donovan Johnson, May 17 2010]
Except for a(1), all terms appear to be of the form p+1 for some prime p. - Chai Wah Wu, Dec 06 2019

			1+443 = 1+443 = 5+439 = 13+431 = 55+389 = 233+211 = 377+67 are n=7 distinct representations of k=444.

Cf. A168382, A169790.

a(12)-a(15) from Max Alekseyev, May 15 2010
a(16)-a(17) from Donovan Johnson, May 17 2010
A prime index in the comment corrected by R. J. Mathar, Jun 02 2010
a(18) from Chai Wah Wu, Dec 06 2019
a(19)-a(21) from Giovanni Resta, Dec 10 2019

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

Original entry on oeis.org

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

Offset: 1

Jason Earls, Nov 24 2009

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]

			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.

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

Cf. A132144, A169790, A169791.

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

cp's OEIS Frontend

A169791 Least number k having n distinct representations as the sum of a nonzero Fibonacci number and a prime.

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