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A370457
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a(n) = n - A368887(n) is the neutron number of the nuclide with the lowest energy among the isobars of mass number n.
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3
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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, 15, 16, 16, 16, 17, 18, 18, 20, 20, 20, 20, 22, 22, 22, 23, 24, 24, 24, 25, 26, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 32, 32, 33, 34, 34, 36, 36, 36, 37, 38, 38, 38, 40, 40, 41, 42
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OFFSET
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1,4
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COMMENTS
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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.
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.
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.
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
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LINKS
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CROSSREFS
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KEYWORD
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nonn,hard,fini
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AUTHOR
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STATUS
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approved
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