A079677 -id:A079677 - cp's OEIS frontend

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

Jonathan Vos Post, Aug 04 2009

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.

			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.

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

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

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

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 *)

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

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

A182487 Nextprime(F(n)) - prevprime(F(n)), where F(n) is the n-th Fibonacci number.

Original entry on oeis.org

3, 4, 4, 6, 4, 6, 6, 14, 10, 10, 6, 6, 8, 18, 12, 24, 16, 10, 6, 12, 30, 12, 24, 42, 30, 24, 60, 24, 30, 34, 30, 36, 46, 12, 36, 18, 34, 24, 24, 30, 36, 52, 72, 16, 22, 48, 44, 50, 34, 20, 20, 28, 44, 50, 40, 92, 60, 86, 16, 52, 48, 66, 46, 168, 50, 174, 36

Offset: 4

Alex Ratushnyak, May 02 2012

Smallest prime following Fibonacci(n) minus largest prime immediately preceding Fibonacci(n). Starting from Fibonacci(4), because for n<4 there is no prime preceding Fibonacci(n).

			a(0) = A014208(4) - A180422(0) = 5 - 2 = 3,
a(7) = A014208(11) - A180422(7) = 97-83 = 14.

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Cf. A014208, A180422, A013633, A058043, A058054, A161503.

Cf. A079677 (distance from F(n) to the nearest prime).

a:= n-> (f-> nextprime(f)-prevprime(f))(combinat[fibonacci](n)):
seq(a(n), n=4..100);  # Alois P. Heinz, Jul 29 2015

Table[f = Fibonacci[n]; NextPrime[f] - NextPrime[f, -1], {n, 4, 100}] (* T. D. Noe, May 02 2012 *)

a(n) = A014208(n+4) - A180422(n).

cp's OEIS Frontend

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

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