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A248974 Floor( 1/(n*sinh(1/n) + n*sin(1/n) - 2) ). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 29 07:08 EDT 2020. Contains 337425 sequences. (Running on oeis4.)