A159977 a(n) = (smallest prime >= Fibonacci(n)) - Fibonacci(n).

1, 1, 0, 0, 0, 3, 0, 2, 3, 4, 0, 5, 0, 2, 3, 4, 0, 7, 20, 14, 3, 2, 0, 13, 4, 10, 11, 16, 0, 23, 4, 4, 25, 10, 14, 35, 6, 24, 3, 2, 6, 7, 0, 20, 9, 48, 0, 5, 28, 18, 23, 14, 14, 11, 16, 10, 21, 4, 62, 13, 38, 12, 7, 16, 12, 19, 36, 28, 143, 32, 58, 29, 96, 100, 33, 2, 30, 27, 12, 62, 25, 46, 0

Offset: 1

Author

Enoch Haga, Apr 28 2009

Keywords

• easy
• nonn

Examples

			a(1) = a(2) = 1 because Fibonacci(1) = Fibonacci(2) = 1, the smallest prime >= 1 is 2, and 2 - 1 = 1.
a(3) = a(4) = a(5) = 0 because Fibonacci(3)=2, Fibonacci(4)=3, and Fibonacci(5)=5 are all prime.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A001605, A159978.

Programs

Maple

a:= n-> (f-> nextprime(f-1)-f)(combinat[fibonacci](n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 04 2018

Mathematica

Table[If[PrimeQ[n],0,NextPrime[n]-n],{n,Fibonacci[Range[90]]}] (* Harvey P. Dale, Jul 22 2016 *)

PARI

F=1;G=0;for(i=1,100,print1(nextprime(F)-F,",");T=F;F+=G;G=T) \\ Hagen von Eitzen, Jul 20 2009

UBASIC

10 'FiboA 20 A=1:print A; 30 B=1:print B; 40 C=A+B:print C;:T=T+1 41 if C<>prmdiv(C) then print "<";nxtprm(C)-C;">":else print "<";0;">"; 50 D=B+C:print D; 51 if D<>prmdiv(D) then print "<";nxtprm(D)-D;">":else print "<";0;">"; 60 A=C:B=D:if T>22 then stop:else 40

Formula

a(n) = (smallest prime >= Fibonacci(n)) - Fibonacci(n).

a(n) = 0 <=> n in { A001605 }. - Alois P. Heinz, Feb 04 2018

Extensions

More terms (cf. b-file) from Hagen von Eitzen, Jul 20 2009

Edited by Jon E. Schoenfield, Feb 04 2018