A169790 - OEIS

%I #13 Apr 28 2019 18:17:29

%S 3,4,10,24,74,444,1614,15684,29400,50124,259224,5332128,11110428,

%T 50395440,451174728,1296895890

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

%C Variant of A168382.

%C 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.

%C This matters because of the existence of Fibonacci primes (see A005478).

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

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

%Y Cf. A168382, A169791.

%K more,nonn

%O 1,1

%A _R. J. Mathar_ and _Jon E. Schoenfield_, May 14 2010

%E a(8)-a(14) from _Max Alekseyev_, May 15 2010

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

%E Prime index in the comment corrected by _R. J. Mathar_, Jun 02 2010