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 A184836 a(n) = n + floor(n*t) + floor(n/t) + floor(n/t^2) + floor(n/t^3), where t is the pentanacci constant. 5
 2, 6, 9, 14, 17, 21, 24, 30, 33, 37, 40, 45, 48, 52, 55, 61, 64, 68, 71, 76, 79, 83, 87, 92, 95, 99, 102, 107, 110, 113, 118, 122, 125, 129, 133, 137, 140, 145, 149, 153, 156, 160, 164, 168, 171, 176, 180, 184, 187, 191, 195, 199, 202, 207, 211, 215, 218, 223, 226, 229, 234, 238, 242, 245, 249, 253, 257, 260, 265, 269, 273, 276, 280, 284, 288, 292, 296, 300, 304, 307, 311, 315, 319, 323, 327, 331, 335, 338, 342, 345, 349, 353, 358, 361, 365, 368, 373, 376, 381, 384, 389, 392, 396, 399, 404, 407, 412, 415, 420, 423 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is one of five sequences that partition the positive integers. Given t is the pentanacci constant, then the following sequences are disjoint: . A184835(n) = n + [n/t] + [n/t^2] + [n/t^3] + [n/t^4], . A184836(n) = n + [n*t] + [n/t] + [n/t^2] + [n/t^3], . A184837(n) = n + [n*t] + [n*t^2] + [n/t] + [n/t^2], . A184838(n) = n + [n*t] + [n*t^2] + [n*t^3] + [n/t], . A184839(n) = n + [n*t] + [n*t^2] + [n*t^3] + [n*t^4], where []=floor. This is a special case of Clark Kimberling's results given in A184812. LINKS Table of n, a(n) for n=1..110. FORMULA Limit a(n)/n = t^2 = 3.8649524691694932164414964... a(n) = n + floor(n*p/s) + floor(n*q/s) + floor(n*r/s) + floor(n*u/s), where p=t, q=t^2, r=t^3, s=t^4, u=t^5, and t is the pentanacci constant. EXAMPLE Given t = pentanacci constant, then t^2 = 1 + t + 1/t + 1/t^2 + 1/t^3, t = 1.965948236645..., t^2 = 3.864952469169..., t^3 = 7.598296491482..., t^4 = 14.93785758893..., t^5 = 29.36705478623... PROG (PARI) {a(n)=local(t=real(polroots(1+x+x^2+x^3+x^4-x^5)[1])); n+floor(n*t)+floor(n/t)+floor(n/t^2)+floor(n/t^3)} CROSSREFS Cf. A184835, A184837, A184838, A184839; A184812, A103814. Sequence in context: A297833 A049508 A184824 * A327895 A373327 A096378 Adjacent sequences: A184833 A184834 A184835 * A184837 A184838 A184839 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 23 2011 STATUS approved

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Last modified June 14 05:27 EDT 2024. Contains 373393 sequences. (Running on oeis4.)