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 A184824 a(n) = n + floor(n*t) + floor(n/t) + floor(n/t^2), where t is the tetranacci constant. 4
 2, 6, 9, 14, 17, 21, 24, 29, 32, 36, 39, 44, 47, 50, 54, 58, 61, 65, 69, 73, 76, 80, 84, 88, 91, 95, 100, 102, 106, 110, 114, 117, 121, 125, 129, 132, 136, 140, 144, 147, 152, 154, 158, 161, 166, 169, 173, 176, 181, 184, 188, 191, 196, 200, 203, 207, 210, 214, 217, 222, 225, 229, 232, 237, 240, 244, 248, 252, 255, 258, 262, 266, 269, 273, 277, 281, 284, 288, 292, 296, 300, 304, 307, 310, 314, 318, 322, 325, 329, 333, 337, 340, 345, 348, 352, 355, 359, 362, 366, 369, 374, 377, 381, 384, 389, 392, 396, 401, 404, 408 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is one of four sequences that partition the positive integers. Given t is the tetranacci constant, then the following sequences are disjoint: . A184823(n) = n + [n/t] + [n/t^2] + [n/t^3], . A184824(n) = n + [n*t] + [n/t] + [n/t^2], . A184825(n) = n + [n*t] + [n*t^2] + [n/t], . A184826(n) = n + [n*t] + [n*t^2] + [n*t^3], 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 = 3.7154951693276375317543272... a(n) = n + floor(n*p/r) + floor(n*q/r) + floor(n*s/r), where p=t, q=t^2, r=t^3, s=t^4, and t is the tetranacci constant. EXAMPLE Let t be the tetranacci constant, then t^2 = 1 + t + 1/t + 1/t^2 and: t = 1.92756197548..., t^2 = 3.71549516932..., t^3 = 7.16184720848..., t^4 = 13.8049043532... PROG (PARI) {a(n)=local(t=real(polroots(1+x+x^2+x^3-x^4)[2])); n+floor(n*t)+floor(n/t)+floor(n/t^2)} CROSSREFS Cf. A184823, A184825, A184826; A184812, A086088. Sequence in context: A171866 A297833 A049508 * A184836 A327895 A373327 Adjacent sequences: A184821 A184822 A184823 * A184825 A184826 A184827 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 23 2011 STATUS approved

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Last modified June 20 08:07 EDT 2024. Contains 373512 sequences. (Running on oeis4.)