

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
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OFFSET

1,2


COMMENTS

The nontrivial binomial coefficients are C(n,k), 2 <= k <= n2 (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


LINKS

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.


EXAMPLE

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.


CROSSREFS

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


KEYWORD

nonn,fini,full


AUTHOR

Douglas Latimer, Mar 22 2012


STATUS

approved



