A183201 Least integer k such that Floor(k*f(n+1))>k*f(n), where f(n)=arccosh(n).

1, 2, 1, 4, 3, 2, 3, 5, 9, 1, 6, 4, 7, 3, 7, 2, 7, 5, 3, 7, 4, 5, 6, 8, 12, 21, 1, 17, 11, 8, 7, 6, 5, 9, 4, 7, 13, 3, 8, 5, 7, 9, 11, 23, 2, 13, 9, 7, 5, 13, 8, 17, 3, 10, 7, 11, 4, 13, 9, 5, 11, 6, 13, 7, 8, 9, 10, 12, 14, 18, 23, 34, 61, 1, 42, 28, 21, 16, 14, 12, 11, 9, 17, 8, 7, 13, 6, 17, 11, 5, 14, 9, 13, 21, 4, 15, 11, 7, 17, 10

Offset: 1

Author

Clark Kimberling, Dec 29 2010

Keywords

• nonn

Comments

Equivalently, k is the least positive integer such that there is a rational number H with denominator k for which n < cosh(H) < n+1.

Crossrefs

Cf. A183162, A183164.

Programs

Mathematica

Table[k=1; While[Floor[k*ArcCosh[n+1]]<=k*ArcCosh[n], k++]; k, {n,100}]