A168382 -id:A168382 - 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

A169790 Least number k having n unordered partitions into a nonzero Fibonacci number and a prime.

Original entry on oeis.org

3, 4, 10, 24, 74, 444, 1614, 15684, 29400, 50124, 259224, 5332128, 11110428, 50395440, 451174728, 1296895890

Offset: 1

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

Variant of A168382.
Fibonacci(1) + prime(4) = Fibonacci(2) + prime(4) = Fibonacci(4) + prime(3) = Fibonacci(5) + prime(2) = 8 are two "distinct" representations of k=8, because Fibonacci(1) = Fibonacci(2) = 1 is treated as indistinguishable, and Fibonacci(4) = prime(2) = 3 are also indistinguishable: k = 1+7 = 3+5.
This matters because of the existence of Fibonacci primes (see A005478).
a(17) > 10^10. [Donovan Johnson, May 17 2010]

			1+443 = 5+439 = 13+431 = 55+389 = 233+211 = 377+67 are n=6 distinct representations of 444.

Cf. A168382, A169791.

a(8)-a(14) from Max Alekseyev, May 15 2010
a(15)-a(16) from Donovan Johnson, May 17 2010
Prime index in the comment corrected by R. J. Mathar, Jun 02 2010

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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