STATUS
proposed
approved
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Revision History for A210576
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Positive integers that cannot be expressed as sum of one or more nontrivial binomial coefficients.
(history; published version)
(history; published version)
STATUS
editing
proposed
EXAMPLE
The lowest 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.
STATUS
proposed
editing
STATUS
editing
proposed
NAME
Natural numbers Positive integers that cannot be expressed as sum of one or more nontrivial binomial coefficients.
STATUS
proposed
editing
STATUS
editing
proposed
COMMENTS
Note that the author this sequence allows the same binomial coefficient to be used multiple times. - T. D. Noe, Apr 12 2013
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 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. 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 seriessequence.
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed