A061045 Numerator of 1/36 - 1/n^2.

-35, -2, -1, -5, -11, 0, 13, 7, 5, 4, 85, 1, 133, 10, 7, 55, 253, 2, 325, 91, 5, 28, 493, 5, 589, 40, 77, 187, 805, 2, 925, 247, 13, 70, 1189, 35, 1333, 88, 55, 391, 1645, 4, 1813, 475, 221, 130, 2173, 7, 2365, 154, 95, 667, 2773, 20, 2989, 775, 119, 208, 3445, 11, 3685, 238, 437, 1015, 4189, 10

Offset

1,1

Comments

Sixth case of Rydberg's formula. From Humphrey's spectrum of hydrogen. See A045944, A000567, A061043, A061046, A061047. - Paul Curtz, Dec 08 2008

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Curtis J. Humphreys, The Sixth Series in the Hydrogen Spectrum, Journal of the Optical Society of America, 1952, 42, p. 432.

Example

The fractions are -35/36, -2/9, -1/12, -5/144, -11/900, 0, 13/1764, 7/576, 5/324, 4/225, 85/4356, 1/48, 133/6084, 10/441, 7/300, 55/2304, 253/10404, 2/81, 325/12996, ...

Mathematica

Numerator[(1/36-1/Range[100]^2)] (* Harvey P. Dale, Mar 17 2013 *)

Prog

(Haskell)
import Data.Ratio ((%), numerator)
a061045 = numerator . (1 % 36 -) . recip . (^ 2) . fromIntegral
-- Reinhard Zumkeller, Jan 06 2014
(Magma) [Numerator(1/6^2 -1/n^2): n in [1..80]]; // G. C. Greubel, Feb 24 2023
(SageMath)
def A061045(n): return ((n^2-36)/(6*n)^2).numerator()
[A061045(n) for n in range(1, 81)] # G. C. Greubel, Feb 24 2023

Crossrefs

A061046 gives denominators.

Cf. A000567, A045944, A061035 - A061050.

Sequence in context: A176199 A059023 A327004 * A350805 A331040 A272683

Adjacent sequences: A061042 A061043 A061044 * A061046 A061047 A061048

Keyword

sign,frac

Author

N. J. A. Sloane, May 26 2001

Status

approved