This site is supported by donations to The OEIS Foundation.

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .