A247357 Least m such that (4/m^2)*Sum_{k=0..m} sqrt(m^2 - k^2) < Pi + 1/n.

1, 3, 5, 7, 8, 10, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 33, 35, 37, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120

Offset

1,2

Comments

a(n+1) - a(n) is in {1,2} for n >= 1.

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 17.

Links

Clark Kimberling, Table of n, a(n) for n = 1..200

Mathematica

z = 200; s[m_] := s[m] = (4/m^2) Sum[Sqrt[m^2 - k^2], {k, 0, m}]
f[n_] := f[n] = Select[Range[z], s[#] < Pi + 1/n &, 1]
u = Flatten[Table[f[n], {n, 1, z}]]

Crossrefs

easy

Sequence in context: A187841 A253301 A003144 * A191251 A285594 A191230

Adjacent sequences: A247354 A247355 A247356 * A247358 A247359 A247360

Keyword

nonn,easy

Author

Clark Kimberling, Sep 24 2014

Status

approved