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A330179
a(n) = n + floor(ns/r) + floor(nt/r), where r = e - 1, s = e, t = e + 1.
2
4, 9, 13, 18, 22, 27, 33, 37, 42, 46, 51, 55, 61, 66, 70, 75, 79, 84, 90, 94, 99, 103, 108, 112, 118, 123, 127, 132, 136, 141, 147, 151, 156, 160, 165, 169, 175, 180, 184, 189, 193, 198, 204, 208, 213, 217, 222, 226, 232, 237, 241, 246, 250, 255, 261, 265
OFFSET
1,1
COMMENTS
This is one of three sequences that partition the positive integers. In general, suppose that r, s, t are positive real numbers for which the sets {i/r: i>=1}, {j/s: j>=1}, {k/t: k>=1} are disjoint. Let a(n) be the rank of n/r when all the numbers in the three sets are jointly ranked. Define b(n) and c(n) as the ranks of n/s and n/t. It is easy to prove that
a(n)=n+[ns/r]+[nt/r],
b(n)=n+[nr/s]+[nt/s],
c(n)=n+[nr/t]+[ns/t], where []=floor.
Taking r = e - 1, s = e, t = e + 1 yields
FORMULA
a(n) = n + floor(ns/r) + floor(nt/r), where r = e - 1, s = e, t = e + 1.
MATHEMATICA
r = E - 1; s = E; t = E + 1;
a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
c[n_] := n + Floor[n*r/t] + Floor[n*s/t]
Table[a[n], {n, 1, 120}] (* A330179 *)
Table[b[n], {n, 1, 120}] (* A016789 *)
Table[c[n], {n, 1, 120}] (* A330180 *)
CROSSREFS
Sequence in context: A330183 A312933 A206908 * A312934 A312935 A312936
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 05 2020
STATUS
approved