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

%I A163768 #13 May 19 2019 04:02:31
%S A163768 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,
%T A163768 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,
%U A163768 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
%N A163768 Distance of Fibonacci(n) to the closest prime which is not Fibonacci(n) itself.
%C A163768 The closest prime to F(n) -- next closest if F(n) itself is prime -- for n = 0, 1, 2, 3, 4, ...:
%C A163768 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.
%H A163768 G. C. Greubel, <a href="/A163768/b163768.txt">Table of n, a(n) for n = 0..1000</a>
%F A163768 For n not in A001605: a(n) = MIN{|A000045(n) - A000040(i)} = A079677(n).
%F A163768 For n in A001605: a(n) = MIN{k such that k > 0 and |A000045(n) - A000040(i)| = k}.
%F A163768 a(n) = A051700(A000045(n)). - _R. J. Mathar_, Aug 06 2009
%e A163768 a(0) = 2 because 2 is the closest prime to F(0) = 0, and 2-0 = 2.
%e A163768 a(1) = 1 because 2 is the closest prime to F(1) = 1, and 2-1 = 1.
%e A163768 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.
%p A163768 A051700 := proc(n) if n < 2 then 2-n; elif n = 2 then 1 ; else min( nextprime(n)-n, n-prevprime(n) ); fi; end:
%p A163768 A000045 := proc(n) combinat[fibonacci](n) ; end:
%p A163768 A163768 := proc(n) A051700(A000045(n)) ; end: seq(A163768(n), n=0..100) ; # _R. J. Mathar_, Aug 06 2009
%t A163768 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 *)
%Y A163768 Cf. A000040, A000045, A001605, A005478, A023186.
%K A163768 easy,nonn
%O A163768 0,1
%A A163768 _Jonathan Vos Post_, Aug 04 2009
%E A163768 More terms from _R. J. Mathar_, Aug 06 2009, reformatted Aug 29 2009