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 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 (list; graph; refs; listen; history; text; internal format)
 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 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=m-complete[i-1])]; ptable); decimal[n_Integer] := (gentable[n]; Sum[2^(k-1)*ptable[[k]], {k, 1, Length[ptable]}]); Table[IntegerString[decimal[s], 2], {s, 0, 100}] CROSSREFS Cf. A000124, A072638. Sequence in context: A136836 A136827 A136831 * A043681 A234472 A139707 Adjacent sequences:  A204006 A204007 A204008 * A204010 A204011 A204012 KEYWORD nonn AUTHOR Frank M Jackson, Jan 09 2012 STATUS approved

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Last modified May 29 10:41 EDT 2020. Contains 334699 sequences. (Running on oeis4.)