%I #22 Mar 19 2024 08:31:55
%S 0,1,1,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,10,10,11,12,12,12,13,14,14,14,
%T 15,16,16,16,17,18,18,20,20,20,20,22,22,22,23,24,24,24,25,26,27,28,28,
%U 28,29,30,30,30,31,32,32,32,33,34,34,36,36,36,37,38,38,38,40,40,41,42
%N a(n) = n - A368887(n) is the neutron number of the nuclide with the lowest energy among the isobars of mass number n.
%C Note that a(146) = 84 corresponds to the unstable nuclide samarium-146 (which has lower energy) rather than the stable nuclide neodymium-146. Likewise, a(247) = 150 corresponds to the nuclide berkelium-247 instead of curium-247 whose half-life is longer by four orders of magnitude.
%C A beta-stable nuclide with an odd number of protons or an odd number of neutrons must have the lowest energy among its isobars. (A beta-stable nuclide is a nuclide whose beta decay (beta-minus and beta-plus decay) is energetically disallowed; that is to say, a nuclide that has lower energy than its isobars with one more or one less proton. Note that double beta decay is allowed.) As a result, an odd number N appears in this sequence exactly A368860(N) times. The missing numbers are the odd terms of A370460.
%C The even numbers that appear only once are the even terms of A370460, except that 54 (96Mo and 98Ru) and 84 (144Nd and 146Sm, the latter being non-primordial) each appears twice; these two numbers surround the elements Tc and Pm which have no beta-stable isotopes. Page 12 of the Zagrebaev et al. link predicts that Nh has no beta-stable isotopes, implying that one of 180 and 182 would be in A370460 but would appear twice in this sequence, depending on which of 294Cn and 294Fl has lower energy.
%C Among the known terms, most numbers appear at most 3 times in this sequence. The exceptions are that 20 occurs 4 times (corresponding to 36S, 37Cl, 38Ar, and 39K), and that 82 occurs 5 times (138Ba, 139La, 140Ce, 141Pr, and 142Nd). - _Jianing Song_, Mar 19 2024
%H Jianing Song, <a href="/A370457/b370457.txt">Table of n, a(n) for n = 1..260</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Beta-decay_stable_isobars">Beta-decay stable isobars</a>.
%H Valeriy Zagrebaev et al., <a href="https://iopscience.iop.org/article/10.1088/1742-6596/420/1/012001">Future of superheavy element research: Which nuclei could be synthesized within the next few years?</a>, Journal of Physics: Conference Series, 420 (March 2013).
%Y Cf. A368887 (atomic numbers), A370460.
%Y Cf. A368859 (beta-stable isotopes), A368860 (isotones), A367461 (isodiaphers).
%K nonn,hard,fini
%O 1,4
%A _Jianing Song_, Feb 18 2024