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A061045
Numerator of 1/36 - 1/n^2.
12
-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
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.
Sequence in context: A176199 A059023 A327004 * A350805 A331040 A272683
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, May 26 2001
STATUS
approved