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A110091
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Denominators of sequence of rationals defined by r(n) = n for n<=1 and for n>1: r(n) = (sum of denominators of r(n-1) and r(n-2))/(sum of numerators of r(n-1) and r(n-2)).
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2
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1, 1, 1, 3, 1, 3, 5, 1, 5, 7, 1, 7, 9, 1, 9, 11, 1, 11, 13, 1, 13, 15, 1, 15, 17, 1, 17, 19, 1, 19, 21, 1, 21, 23, 1, 23, 25, 1, 25, 27, 1, 27, 29, 1, 29, 31, 1, 31, 33, 1, 33, 35, 1, 35, 37, 1, 37, 39, 1, 39, 41, 1, 41, 43, 1, 43, 45, 1, 45, 47, 1, 47, 49, 1, 49, 51, 1, 51, 53, 1, 53, 55
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OFFSET
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0,4
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LINKS
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FORMULA
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a(3*k) = 2*k+1, a(3*k+1) = 1, a(3*k+2) = 2*k+1.
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MATHEMATICA
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a[n_]:= a[n]= If[Mod[n, 3]==0, 2*Floor[n/3] +1, If[Mod[n, 3]==1, 1, 2*Floor[n/3] +1]]; Table[a[n], {n, 0, 100}] (* G. C. Greubel, Jun 16 2021 *)
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PROG
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(Sage)
if (n%3==0): return 2*(n//3) + 1
elif (n%3==1): return 1
else: return 2*(n//3) +1
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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