A163768 Distance of Fibonacci(n) to the closest prime which is not Fibonacci(n) itself.

2, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 6, 5, 4, 2, 3, 4, 4, 5, 4, 2, 3, 2, 4, 13, 4, 10, 11, 14, 10, 23, 4, 4, 9, 10, 14, 11, 6, 12, 3, 2, 6, 7, 12, 16, 9, 24, 6, 5, 20, 18, 23, 14, 6, 9, 12, 10, 21, 4, 30, 13, 38, 4, 7, 16, 12, 19, 36, 22, 31, 4, 32, 11, 12, 60, 7, 2, 6, 27, 12, 62, 25, 20, 6, 19, 78

Offset: 0

Author

Jonathan Vos Post, Aug 04 2009

Keywords

• easy
• nonn

Comments

The closest prime to F(n) -- next closest if F(n) itself is prime -- for n = 0, 1, 2, 3, 4, ...:

2, 2, 2, 3, 2, 3 or 7, 7, 11, 19 or 23, 31 or 37, 53, 83, 139 or 149, 229, 379, 607 or 613.

Examples

			a(0) = 2 because 2 is the closest prime to F(0) = 0, and 2-0 = 2.
a(1) = 1 because 2 is the closest prime to F(1) = 1, and 2-1 = 1.
a(3) = 1 because 3 is the closest prime to F(3) = 2 other than the prime F(3) = 2 itself, and 3-2 = 1.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000040, A000045, A001605, A005478, A023186.

Programs

Maple

A051700 := proc(n) if n < 2 then 2-n; elif n = 2 then 1 ; else min( nextprime(n)-n, n-prevprime(n) ); fi; end:
A000045 := proc(n) combinat[fibonacci](n) ; end:
A163768 := proc(n) A051700(A000045(n)) ; end: seq(A163768(n), n=0..100) ; # R. J. Mathar, Aug 06 2009

Mathematica

g[n_]:=Module[{fn=Fibonacci[n],a,b},a=NextPrime[fn,-1];b=NextPrime[fn];Min[Abs[fn-a],Abs[b-fn]]]; Table[g[i],{i,0,100}] (* Harvey P. Dale, Jan 15 2011 *)

Formula

For n not in A001605: a(n) = MIN{|A000045(n) - A000040(i)} = A079677(n).

For n in A001605: a(n) = MIN{k such that k > 0 and |A000045(n) - A000040(i)| = k}.

a(n) = A051700(A000045(n)). - R. J. Mathar, Aug 06 2009

Extensions

More terms from R. J. Mathar, Aug 06 2009, reformatted Aug 29 2009