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A210576
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Positive integers that cannot be expressed as sum of one or more nontrivial binomial coefficients.
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1
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1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 17, 19, 23, 29
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OFFSET
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1,2
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COMMENTS
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The nontrivial binomial coefficients are C(n,k), 2 <= k <= n-2 (A006987).
I conjectured that the sequence is finite, consisting of the terms listed.
Note that this sequence allows the same binomial coefficient to be used multiple times. - T. D. Noe, Apr 12 2013
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
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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A210578 contains many of the integers that cannot be elements of this sequence.
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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