A245472 Number of composite Lucas numbers between the prime Lucas numbers A005479(n) and A005479(n+1).

0, 1, 0, 1, 0, 2, 1, 2, 0, 1, 11, 5, 3, 5, 5, 7, 9, 7, 33, 199, 39, 149, 109, 3, 245, 233, 263, 3425, 5, 1057, 1889, 725, 2223, 1559, 1711, 485, 5019, 15979, 1329, 7727, 6661, 4833, 25667, 8177, 4973, 45233, 8033, 11429, 23567, 10111, 9465, 141625, 43139, 56175

Offset: 1

Author

Michel Lagneau, Jul 23 2014

Keywords

• nonn

Examples

			a(1)=0 because A005479(1)= 2, A005479(2)= 3 and there are no composite Lucas number between 2 and 3 (the number 1 is not composite).
a(6)=2 because A005479(6)= 47, A005479(7)= 199 and there are 2 composite Lucas numbers between 47 and 199: 76 = 2^2*19 and 123 = 3*41.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..63

Crossrefs

Cf. A000032, A001606, A245470.

Programs

Maple

with(combinat,fibonacci):with(numtheory):i:=0:a:=n->2*fibonacci(n-1)+fibonacci(n):for n from 3 to 100 do:if type (a(n), prime)=true then printf(`%d, `, i):i:=0:else i:=i+1:fi:od:

Formula

a(n) = A001606(n+1) - A001606(n) - 1, for n > 1.