A061043 Numerator of 1/25 - 1/n^2.

0, 11, 24, 39, 56, 3, 96, 119, 144, 171, 8, 231, 264, 299, 336, 3, 416, 459, 504, 551, 24, 651, 704, 759, 816, 7, 936, 999, 1064, 1131, 48, 1271, 1344, 1419, 1496, 63, 1656, 1739, 1824, 1911, 16, 2091, 2184, 2279, 2376, 99, 2576, 2679, 2784

Offset: 5

Author

N. J. A. Sloane, May 26 2001

Keywords

• nonn
• easy
• frac
• nice

Comments

From Pfund spectrum of hydrogen. Wavelengths in hydrogen spectrum are given by Rydberg's formula 1/wavelength = constant*(1/m^2 - 1/n^2).

a(n) = (n+5)^2-25 = n*(n+10) except a(5p) for p positive. Second (with m=5) of this kind after A061039, Paschen (m=3) and before A061047, Hansen-Strong (m=7). For the fourth, what is the value of m in 1/m^2-1/n^2? m=9? - Paul Curtz, Nov 01 2008

References

• J. E. Brady and G. E. Humiston, General Chemistry, 3rd. ed., Wiley; p. 78.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 5..10000
• J. J. O'Connor and E. F. Robertson, Johannes Robert Rydberg
• Eric Weisstein's World of Physics, Balmer Formula

Crossrefs

Cf. A061035-A061050.

Programs

Haskell

import Data.Ratio ((%), numerator)
a061043 = numerator . (1 % 25 -) . recip . (^ 2) . fromIntegral
-- Reinhard Zumkeller, Jan 06 2014

Mathematica

Numerator[1/25-1/Range[5,60]^2] (* Harvey P. Dale, Jan 28 2013 *)

PARI

a(n)=numerator(1/25 - 1/n^2) \\ Charles R Greathouse IV, Feb 06 2017

Python

from fractions import Fraction
def a(n): return (Fraction(1, 25) - Fraction(1, n*n)).numerator
print([a(n) for n in range(5, 54)]) # Michael S. Branicky, Nov 19 2021