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%I #41 Jul 26 2022 23:34:20
%S 1,2,3,4,5,7,8,9,11,13,14,17,19,23,29
%N Positive integers that cannot be expressed as sum of one or more nontrivial binomial coefficients.
%C The nontrivial binomial coefficients are C(n,k), 2 <= k <= n-2 (A006987).
%C I conjectured that the sequence is finite, consisting of the terms listed.
%C This conjecture is now proved. - _Douglas Latimer_, Apr 10 2013
%C Note that this sequence allows the same binomial coefficient to be used multiple times. - _T. D. Noe_, Apr 12 2013
%C 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 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 Douglas Latimer, <a href="/A210576/a210576.txt">Computation of Terms <= 30</a>.
%H Douglas Latimer, <a href="/A210576/a210576_1.txt">Terms Listed Are the Entire Sequence</a>.
%e 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 A210578 contains many of the integers that cannot be elements of this sequence.
%Y Cf. A006987 and A007318.
%Y Positions of zeros in A008651. Cf. A005796.
%K nonn,fini,full
%O 1,2
%A _Douglas Latimer_, Mar 22 2012
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