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 A190504 n+[ns/r]+[nt/r]+[nu/r]; r=golden ratio, s=r+1, t=r+2, u=r+3. 4
 6, 14, 21, 29, 38, 45, 52, 59, 68, 76, 83, 91, 100, 106, 114, 121, 130, 138, 145, 153, 159, 168, 176, 183, 191, 200, 207, 214, 221, 230, 238, 245, 253, 262, 268, 276, 283, 291, 300, 307, 315, 321, 330, 338, 345, 353, 362, 368, 376, 383, 392, 400, 407, 415, 421, 430, 438, 445, 453, 462, 469, 476, 483, 492, 500, 507, 515, 524, 530 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is one of four sequences that partition the positive integers.  In general, suppose that r, s, t, u are positive real numbers for which the sets {i/r: i>=1}, {j/s: j>=1}, {k/t: k>=1, {h/u: h>=1} are pairwise disjoint.  Let a(n) be the rank of n/r when all the numbers in the four sets are jointly ranked.  Define b(n), c(n), d(n) as the ranks of n/s, n/t, n/u, respectively.  It is easy to prove that a(n)=n+[ns/r]+[nt/r]+[nu/r], b(n)=n+[nr/s]+[nt/s]+[nu/s], c(n)=n+[nr/t]+[ns/t]+[nu/t], d(n)=n+[nr/u]+[ns/u]+[nt/u], where []=floor. Taking r=golden ratio, s=r+1, t=r+2, u=r+3 gives a=A190504, b=A190505, c=A190506, d=A190507. LINKS MATHEMATICA r=GoldenRatio; s=r+1; t=r+2; u=r+3; a[n_] := n + Floor[n*s/r] + Floor[n*t/r]+Floor[n*u/r]; b[n_] := n + Floor[n*r/s] + Floor[n*t/s]+Floor[n*u/s]; c[n_] := n + Floor[n*r/t] + Floor[n*s/t]+Floor[n*u/t]; d[n_] := n + Floor[n*r/u] + Floor[n*s/u]+Floor[n*t/u]; Table[a[n], {n, 1, 120}]  (*A190504*) Table[b[n], {n, 1, 120}]  (*A190505*) Table[c[n], {n, 1, 120}]  (*A190506*) Table[d[n], {n, 1, 120}]  (*A190507*) CROSSREFS Cf. A190505, A190506, A190507 (the other three sequences in the partition of N). Sequence in context: A063299 A184924 A110223 * A175582 A182081 A125086 Adjacent sequences:  A190501 A190502 A190503 * A190505 A190506 A190507 KEYWORD nonn AUTHOR Clark Kimberling, May 11 2011 STATUS approved

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Last modified August 16 10:10 EDT 2022. Contains 356161 sequences. (Running on oeis4.)