A248974 Floor( 1/(n*sinh(1/n) + n*sin(1/n) - 2) ).

59, 959, 4859, 15359, 37499, 77759, 144059, 245759, 393659, 599999, 878459, 1244159, 1713659, 2304959, 3037499, 3932159, 5011259, 6298559, 7819259, 9599999, 11668859, 14055359, 16790459, 19906559, 23437499, 27418559, 31886459, 36879359, 42436859, 48599999

Offset

1,1

Comments

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.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = 60*n^4 - 1.

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

G.f.: x*(x^4-64*x^3-654*x^2-664*x-59) / (x-1)^5. - Colin Barker, Oct 22 2014

Mathematica

Table[Floor[1/(n*Sinh[1/n] + n*Sin[1/n] - 2)], {n, 1, 60}]

Prog

(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
(Magma) [Floor(1/(n*Sinh(1/n) + n*Sin(1/n) - 2)): n in [1..30]]; // Vincenzo Librandi, Oct 23 2014

Crossrefs

Cf. A000583.

Sequence in context: A215433 A093259 A336576 * A245941 A248620 A210398

Adjacent sequences: A248971 A248972 A248973 * A248975 A248976 A248977

Keyword

nonn,easy

Author

Clark Kimberling, Oct 19 2014

Status

approved