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