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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

%I

%S 2,6,9,14,17,21,24,30,33,37,40,45,48,52,55,61,64,68,71,76,79,83,87,92,

%T 95,99,102,107,110,113,118,122,125,129,133,137,140,145,149,153,156,

%U 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

%N a(n) = n + floor(n*t) + floor(n/t) + floor(n/t^2) + floor(n/t^3), where t is the pentanacci constant.

%C This is one of five sequences that partition the positive integers.

%C Given t is the pentanacci constant, then the following sequences are disjoint:

%C . A184835(n) = n + [n/t] + [n/t^2] + [n/t^3] + [n/t^4],

%C . A184836(n) = n + [n*t] + [n/t] + [n/t^2] + [n/t^3],

%C . A184837(n) = n + [n*t] + [n*t^2] + [n/t] + [n/t^2],

%C . A184838(n) = n + [n*t] + [n*t^2] + [n*t^3] + [n/t],

%C . A184839(n) = n + [n*t] + [n*t^2] + [n*t^3] + [n*t^4], where []=floor.

%C This is a special case of Clark Kimberling's results given in A184812.

%F Limit a(n)/n = t^2 = 3.8649524691694932164414964...

%F 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.

%e Given t = pentanacci constant, then t^2 = 1 + t + 1/t + 1/t^2 + 1/t^3,

%e t = 1.965948236645..., t^2 = 3.864952469169..., t^3 = 7.598296491482..., t^4 = 14.93785758893..., t^5 = 29.36705478623...

%o (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)}

%Y Cf. A184835, A184837, A184838, A184839; A184812, A103814.

%K nonn

%O 1,1

%A _Paul D. Hanna_, Jan 23 2011

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Last modified November 28 04:05 EST 2021. Contains 349400 sequences. (Running on oeis4.)