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A163768
Distance of Fibonacci(n) to the closest prime which is not Fibonacci(n) itself.
1
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
0,1
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
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
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