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%I #14 Sep 08 2022 08:46:10
%S 59,959,4859,15359,37499,77759,144059,245759,393659,599999,878459,
%T 1244159,1713659,2304959,3037499,3932159,5011259,6298559,7819259,
%U 9599999,11668859,14055359,16790459,19906559,23437499,27418559,31886459,36879359,42436859,48599999
%N Floor( 1/(n*sinh(1/n) + n*sin(1/n) - 2) ).
%C When the numbers k*sinh[1/k] - 1 and 1 - k*sin[1/k], for k >=1, are jointly ranked, the former occupy positions 1,3,5,7,... and the latter occupy positions 2,4,6,8,... The difference between neighbors is n*Sinh[1/n] + n*Sin[1/n] - 2, so that A248968 represents the closeness between neighbors. All the terms end in 9.
%H Clark Kimberling, <a href="/A248974/b248974.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 60*n^4 - 1.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Colin Barker_, Oct 22 2014
%F G.f.: x*(x^4-64*x^3-654*x^2-664*x-59) / (x-1)^5. - _Colin Barker_, Oct 22 2014
%t Table[Floor[1/(n*Sinh[1/n] + n*Sin[1/n] - 2)], {n, 1, 60}]
%o (PARI) Vec(x*(x^4-64*x^3-654*x^2-664*x-59)/(x-1)^5 + O(x^100)) \\ _Colin Barker_, Oct 22 2014
%o (Magma) [Floor(1/(n*Sinh(1/n) + n*Sin(1/n) - 2)): n in [1..30]]; // _Vincenzo Librandi_, Oct 23 2014
%Y Cf. A000583.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Oct 19 2014
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