cp's OEIS Frontend

A110976 Sequence of numerators associated with the continued fraction based on the sequence d(n)= distance of n from closest prime ( A051699).

%I A110976 #9 Sep 04 2014 08:00:58
%S A110976 2,3,2,3,5,3,8,3,11,25,36,25,61,25,86,197,283,197,480,197,677,1551,
%T A110976 2228,1551,3779,9109,31106,71321,102427,71321,173748,71321,245069,
%U A110976 561459,1929446,4420351,6349797,4420351,10770148,25960647,36730795,25960647
%N A110976 Sequence of numerators associated with the continued fraction based on the sequence d(n)= distance of n from closest prime ( A051699).
%C A110976 The value of the continued fraction (for n to infinity) is 2.77459638163600405370875399896...; A(n) = A(n+2) if d(n) =2 and d(n+2) = 0
%D A110976 G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 110.
%F A110976 See program
%e A110976 if n = 2, A(n) = A(2) = 3 because A(0) = 2, A(1) = 1 * A(0) + 1 = 3, as the distances of n from closest prime are 2, 1, 0, 0, 1 ...
%p A110976 A[0]:=d[0]; A[1]:=d[1]*A[0]+1; B[0]:=1; B[1]:=d[1]*B[0]; for n from 2 by 1 to N do A[n]:=d[n]*A[n-1]+A[n-2]; B[n]:=d[n]*B[n-1]+B[n-2]; od;
%Y A110976 Cf. A051699, A109139, A109140, A110977.
%K A110976 frac,nonn
%O A110976 0,1
%A A110976 _Giorgio Balzarotti_ and _Paolo P. Lava_, Sep 28 2005