

A204009


a(n) is a binary vector for selecting distinct terms from A000124 that when summed give n; it uses the greedy algorithm.


2



0, 1, 10, 11, 100, 101, 110, 1000, 1001, 1010, 1011, 10000, 10001, 10010, 10011, 10100, 100000, 100001, 100010, 100011, 100100, 100101, 1000000, 1000001, 1000010, 1000011, 1000100, 1000101, 1000110, 10000000, 10000001, 10000010, 10000011, 10000100
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OFFSET

0,3


COMMENTS

a(n) is a binary vector for selecting terms from the complete sequence, A000124 that when summed gives n. It uses the greedy algorithm to select from multiple solutions.


LINKS

Table of n, a(n) for n=0..33.
Wikipedia, Complete sequence.


FORMULA

a(n) x A000124 = n, where x is the inner product and the binary vector is in ascending powers of 2 with infinite trailing zeros.


EXAMPLE

14 can be written as 7+4+2+1, i.e. 1111, or as 11+2+1, i.e. 10011, and the latter is chosen because it uses the greedy algorithm for selection.


MATHEMATICA

complete[m_Integer] := (m(m+1)/2+1); gentable[n_Integer] := (m=n; ptable={0}; While[m!=0, (i=0; While[complete[i]<=m&&ptable[[i+1]]!=1, (AppendTo[ptable, 0]; i++)]; ptable[[i]]=1; m=mcomplete[i1])]; ptable); decimal[n_Integer] := (gentable[n]; Sum[2^(k1)*ptable[[k]], {k, 1, Length[ptable]}]); Table[IntegerString[decimal[s], 2], {s, 0, 100}]


CROSSREFS

Cf. A000124, A072638.
Sequence in context: A136827 A136831 A136836 * A043681 A234472 A139707
Adjacent sequences: A204006 A204007 A204008 * A204010 A204011 A204012


KEYWORD

nonn


AUTHOR

Frank M Jackson, Jan 09 2012


STATUS

approved



