Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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