%I A018227
%S A018227 2,10,18,36,54,86,118
%N A018227 Magic numbers: atoms with full shells containing any of these numbers 
               of electrons are considered stable.
%C A018227 Atomic numbers of noble elements in the periodic table.
%C A018227 Partial sums of A093907. - Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 
               24 2006
%C A018227 Comment from Don N. Page (don(AT)phys.ualberta.ca), Dec 12 2006: (Start)
%C A018227 "Relativistic corrections and instabilities to pair creation of electrons 
               and positrons would occur even if one could have stable nuclei of 
               arbitrarily many protons Z for the fixed value of the fine structure 
               constant alpha ~ 1/137 in our universe.
%C A018227 "However, if one considered an imaginary universe with arbitrarily tiny 
               alpha and a fixed point source of charge Z, one could have stable 
               neutral atoms of Z nonrelativistic electrons of mass m for any Z, 
               so long as one takes the limit Z alpha -> 0 by taking alpha -> 0 
               after fixing Z.
%C A018227 "One could then define noble elements to be given by the integer values 
               of Z such that the ionization energy, in units of m c^2 alpha^2, 
               of any such atom in its ground state with larger Z is less than that 
               of the noble element (which appears to be the case for all the noble 
               elements with the actual nonzero value of alpha).
%C A018227 "This sequence of idealized nonrelativistic noble elements with Z electrons 
               would give an infinite sequence of integers Z, which may or may not 
               be the same as that given by the explicit formula listed for the 
               present sequence. It would likely be a difficult mathematical problem 
               to calculate this infinite sequence." (End)
%D A018227 A brief description is given under "Magic numbers" in the Encyclopedia 
               Brittanica.
%D A018227 S Bjornholm, Clusters..., Contemp. Phys. 31 1990 pp. 309-324 (p. 312).
%H A018227 D. Weise, <a href="http://www.mi.sanu.ac.yu/vismath/weise1/">The Pythagorean 
               Approach to Problems of Periodicity in Chemistry and Nuclear Physics</
               a>
%H A018227 D. Weise, <a href="http://www.mi.sanu.ac.yu/vismath/visbook/weise2">Pythagorean 
               Approach To Problems Of Periodicity In Fermionic System</a>
%F A018227 a(n) = a(n-1) + ((2*n + 3 + (-1)^n)^2)/8; a(n) = (2*n^3 + 12*n^2 + 25*n 
               - 6 + (-1)^n*(3*n + 6))/12 - Warut Roonguthai (warut822(AT)yahoo.com), 
               Jun 20 2005
%F A018227 a(n) = n{(n+3)^2 + 5}/6 for even n, a(n) = n{(n+3)^2 + 2)/6 - 1 [or C(n+3,
               3) - 2, i.e. A000292(n) - 2] for odd n. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Feb 02 2006
%F A018227 Partial sums of A116471. - Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 
               31 2006
%Y A018227 Cf. A018226.
%Y A018227 Sequence in context: A097269 A028413 A082969 this_sequence A092062 A134251 
               A055260
%Y A018227 Adjacent sequences: A018224 A018225 A018226 this_sequence A018228 A018229 
               A018230
%K A018227 nonn,fini,full
%O A018227 1,1
%A A018227 John Raithel (raithel(AT)rahul.net)