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%I #52 Mar 19 2024 08:32:00
%S 1,1,2,2,2,3,3,4,4,5,5,6,6,7,7,8,8,8,9,10,10,10,11,12,12,12,13,14,14,
%T 14,15,16,16,16,17,16,17,18,19,18,19,20,20,20,21,22,22,22,22,22,23,24,
%U 24,24,25,26,26,26,27,28,28,28,29,28,29,30,30,30,31,32,31,32,32,32
%N a(n) is the atomic number of the nuclide with the lowest energy among the isobars of mass number n.
%C Various models agree that a(262) = a(263) = a(264) = 102, while it is unknown whether a(261) = 101 or 102, and whether a(265) = 102 or 103 (note that mendelevium-261, nobelium-261, -263, -264, -265 and lawrencium-265 are all undiscovered).
%C Note that a(146) = 62 corresponds to the unstable nuclide samarium-146 (which has lower energy) rather than the stable nuclide neodymium-146. Likewise, a(247) = 97 corresponds to the nuclide berkelium-247 instead of curium-247 whose half-life is longer by four orders of magnitude.
%C No terms being equal to 43 or 61 corresponds to the fact that there is no beta-stable isotope of technetium and promethium. (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.) Page 12 of the Zagrebaev et al. link predicts further that no terms are equal to 113.
%C 58 is the only known even number to only appear once in this sequence, the corresponding nuclide being cerium-140.
%C Among the known terms, most numbers appear at most 5 times in this sequence. The exceptions are that 50 occurs 7 times (corresponding to mass numbers 114 - 120), and that 62 occurs 6 times (corresponding to mass numbers 146 - 150 and 152, with samarium-146 being non-primordial). - _Jianing Song_, Mar 19 2024
%H Jianing Song, <a href="/A368887/b368887.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).
%e a(5) = 2 because helium-5 has lower energy than hydrogen-5, lithium-5 and (possibly) beryllium-5.
%e a(147) = 62 because samarium-147 has lower energy than promethium-147, europium-147 and so on.
%e a(144) = 60 because between neodymium-144 and samarium-144 (the beta-stable isobars with mass number 144), the former has lower energy.
%e a(148) = 62 because between neodymium-148 and samarium-148 (the beta-stable isobars with mass number 148), the latter has lower energy.
%e a(212) = 84 because between polonium-212 and radon-212 (the beta-stable isobars with mass number 212), the former has lower energy.
%Y Cf. A370457 (neutron numbers).
%Y Cf. A368859 (beta-stable isotopes), A368860 (isotones), A367461 (isodiaphers).
%K nonn,hard,fini
%O 1,3
%A _Jianing Song_, Jan 09 2024
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