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%I A210576 #41 Jul 26 2022 23:34:20
%S A210576 1,2,3,4,5,7,8,9,11,13,14,17,19,23,29
%N A210576 Positive integers that cannot be expressed as sum of one or more nontrivial binomial coefficients.
%C A210576 The nontrivial binomial coefficients are C(n,k), 2 <= k <= n-2 (A006987).
%C A210576 I conjectured that the sequence is finite, consisting of the terms listed.
%C A210576 This conjecture is now proved. - _Douglas Latimer_, Apr 10 2013
%C A210576 Note that this sequence allows the same binomial coefficient to be used multiple times. - _T. D. Noe_, Apr 12 2013
%C A210576 These are the only values of the angular momentum for which a wavefunction with such an angular momentum and the symmetry of a dodecahedron is impossible. [Baez] - _Andrey Zabolotskiy_, Mar 28 2018
%H A210576 John Baez, <a href="https://johncarlosbaez.wordpress.com/2017/12/31/quantum-mechanics-and-the-dodecahedron/">Quantum Mechanics and the Dodecahedron</a>, Dec 31 2017.
%H A210576 Douglas Latimer, <a href="/A210576/a210576.txt">Computation of Terms <= 30</a>.
%H A210576 Douglas Latimer, <a href="/A210576/a210576_1.txt">Terms Listed Are the Entire Sequence</a>.
%e A210576 The smallest terms in the sequence are 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14 because 6, 10 and 15 cannot be terms, as these are the lowest nontrivial binomial coefficients; 12 and 16 cannot be terms, as these are the lowest sums of two nontrivial binomial coefficients; and sums of three or more nontrivial binomial coefficients cannot exclude any of the listed terms.
%Y A210576 A210578 contains many of the integers that cannot be elements of this sequence.
%Y A210576 Cf. A006987 and A007318.
%Y A210576 Positions of zeros in A008651. Cf. A005796.
%K A210576 nonn,fini,full
%O A210576 1,2
%A A210576 _Douglas Latimer_, Mar 22 2012

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