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A208571 Number of non-practical binary partitions of n. 0
0, 1, 0, 2, 1, 3, 0, 4, 2, 6, 2, 8, 5, 11, 0, 10, 4, 14, 4, 18, 10, 24, 6, 26, 14, 34, 16, 42, 27, 53, 0, 36, 10, 46, 8, 54, 22, 68, 12, 72, 30, 90, 32, 106, 56, 130, 26, 120, 52, 146, 54, 168, 88, 202, 80, 220, 122, 262, 134, 300, 187, 353, 0, 202, 36, 238, 20, 258, 66, 304, 24, 308, 78, 362, 68, 398, 136, 466, 52, 442, 124, 514, 112, 562, 202, 652, 160, 684, 266, 790, 272, 870, 402, 1000, 166, 858, 286, 978, 270, 1056 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A practical partition is one in which 1..n can all be represented as a sum of a subset of the members of the partition.

LINKS

Table of n, a(n) for n=1..100.

J. Dixmier and J. L. Nicolas, Partitions without small parts, Colloquia Mathematica Societatis Janos Bolyai 51, Number Theory, Budapest, Hungary, 1987, pp. 9-33.

P. Erdos and J. L. Nicolas, On practical partitions, Collectanea Mathematica 46:1-2 (1995), pp. 57-76.

P. Erdos and M. Szalay, On some problems of J. Denes and P. Turan, Studies in Pure Mathematics to the memory of P. Turan, Editor P. Erdos, Budapest 1983, pp. 187-212.

EXAMPLE

The binary partitions of 4 are 4, 2+2, 2+1+1, and 1+1+1+1; 4 and 2+2 cannot represent 1, but the other two represent all of 1, 2, 3, and 4. Thus a(4) = 2.

CROSSREFS

Cf. A018819.

Sequence in context: A025480 A088002 A030109 * A264520 A058208 A070817

Adjacent sequences:  A208568 A208569 A208570 * A208572 A208573 A208574

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Mar 20 2012

STATUS

approved

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Last modified August 18 14:08 EDT 2017. Contains 290720 sequences.