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A210576 Natural numbers that cannot be expressed as sum of one or more nontrivial binomial coefficients. 1
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 17, 19, 23, 29 (list; graph; refs; listen; history; text; internal format)



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.

This conjecture is now proved. - Douglas Latimer, Apr 10 2013

Note that the author 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


Table of n, a(n) for n=1..15.

John Baez, Quantum Mechanics and the Dodecahedron, Dec 31 2017.

Douglas Latimer, Computation of Terms <= 30.

Douglas Latimer, Terms Listed Are the Entire Sequence.


The lowest terms in the sequence are 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14 . Because:

6, 10 and 15 cannot be elements of the sequence, as these are the lowest nontrivial binomial coefficients.

12 and 16 cannot be elements of the sequence, as these are the lowest sums of two nontrivial binomial coefficients.

Sums of three or more nontrivial binomial coefficients cannot exclude any of the listed terms.


A210578 contains many of the integers that cannot be elements of this series.

Cf. A006987 and A007318.

Positions of zeros in A008651. Cf. A005796.

Sequence in context: A214981 A322030 A326623 * A191848 A293205 A046687

Adjacent sequences:  A210573 A210574 A210575 * A210577 A210578 A210579




Douglas Latimer, Mar 22 2012



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Last modified February 20 20:08 EST 2020. Contains 332084 sequences. (Running on oeis4.)