A163768 - OEIS

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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

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OFFSET

0,1

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.

LINKS

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

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

EXAMPLE

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.

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 *)

CROSSREFS

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

Sequence in context: A111335 A345238 A242442 * A327659 A327519 A287917

Adjacent sequences: A163765 A163766 A163767 * A163769 A163770 A163771

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Aug 04 2009

EXTENSIONS

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

STATUS

approved