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Search: id:A110976
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| A110976 |
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Sequence of numerators associated with the continued fraction based on the sequence d(n)= distance of n from closest prime ( A051699). |
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3
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| 2, 3, 2, 3, 5, 3, 8, 3, 11, 25, 36, 25, 61, 25, 86, 197, 283, 197, 480, 197, 677, 1551, 2228, 1551, 3779, 9109, 31106, 71321, 102427, 71321, 173748, 71321, 245069, 561459, 1929446, 4420351, 6349797, 4420351, 10770148, 25960647, 36730795, 25960647
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OFFSET
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0,1
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COMMENT
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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
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FORMULA
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See program
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EXAMPLE
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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 ...
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MAPLE
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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;
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CROSSREFS
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Cf. A051699 A109139 A109140 A110977.
Sequence in context: A124459 A046147 A052369 this_sequence A151570 A059036 A163466
Adjacent sequences: A110973 A110974 A110975 this_sequence A110977 A110978 A110979
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KEYWORD
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frac,nonn
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AUTHOR
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Giorgio Balzarotti, Paolo P. Lava (greenblue(AT)tiscali.it), Sep 28 2005
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