cp's OEIS Frontend

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

%I A061043 #26 Jul 28 2022 20:27:56
%S A061043 0,11,24,39,56,3,96,119,144,171,8,231,264,299,336,3,416,459,504,551,
%T A061043 24,651,704,759,816,7,936,999,1064,1131,48,1271,1344,1419,1496,63,
%U A061043 1656,1739,1824,1911,16,2091,2184,2279,2376,99,2576,2679,2784
%N A061043 Numerator of 1/25 - 1/n^2.
%C A061043 From Pfund spectrum of hydrogen. Wavelengths in hydrogen spectrum are given by Rydberg's formula 1/wavelength = constant*(1/m^2 - 1/n^2).
%C A061043 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
%D A061043 J. E. Brady and G. E. Humiston, General Chemistry, 3rd. ed., Wiley; p. 78.
%H A061043 Reinhard Zumkeller, <a href="/A061043/b061043.txt">Table of n, a(n) for n = 5..10000</a>
%H A061043 J. J. O'Connor and E. F. Robertson, <a href="http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Rydberg.html">Johannes Robert Rydberg</a>
%H A061043 Eric Weisstein's World of Physics, <a href="http://scienceworld.wolfram.com/physics/BalmerFormula.html">Balmer Formula</a>
%t A061043 Numerator[1/25-1/Range[5,60]^2] (* _Harvey P. Dale_, Jan 28 2013 *)
%o A061043 (Haskell)
%o A061043 import Data.Ratio ((%), numerator)
%o A061043 a061043 = numerator . (1 % 25 -) . recip . (^ 2) . fromIntegral
%o A061043 -- _Reinhard Zumkeller_, Jan 06 2014
%o A061043 (PARI) a(n)=numerator(1/25 - 1/n^2) \\ _Charles R Greathouse IV_, Feb 06 2017
%o A061043 (Python)
%o A061043 from fractions import Fraction
%o A061043 def a(n): return (Fraction(1, 25) - Fraction(1, n*n)).numerator
%o A061043 print([a(n) for n in range(5, 54)]) # _Michael S. Branicky_, Nov 19 2021
%Y A061043 Cf. A061035-A061050.
%K A061043 nonn,easy,frac,nice
%O A061043 5,2
%A A061043 _N. J. A. Sloane_, May 26 2001