A203076 Convert A203075(n) to base 10.

0, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 26, 27, 29, 30, 31, 39, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 58, 59, 61, 62, 63, 67, 69, 70, 71, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 90, 91, 93, 94, 95

Offset: 0

Author

Frank M Jackson and N. J. A. Sloane, Dec 28 2011

Keywords

• nonn

Comments

Any nonnegative number can be written as a sum of distinct terms of the complete sequence, A203074. Terms a(n) are decimal representations of binary vectors (in ascending powers of 2) used to select terms of A203074 that when summed give n.

Links

• Wikipedia, "Complete" sequence. [Wikipedia calls a sequence "complete" (sic) if every positive integer is a sum of distinct terms. This name is extremely misleading and should be avoided. - _N. J. A. Sloane_, May 20 2023]

Crossrefs

Cf. A203074, A203075.

Programs

Mathematica

nextprime[n_Integer] := (k=n+1;While[!PrimeQ[k], k++];k);aprime[m_Integer] := (If[m==0, 1, nextprime[2^(m-1)]]);seqtable[l_] := (stable=Table[aprime[j], {j, 0, l}];stable);inttable[p_] := (itable=Reverse[IntegerDigits[p, 2]];itable);h=1;otable={0};ttable={};While[h<100, (inttable[h];seqtable[Length[itable]-1];test=itable.stable;If[!MemberQ[ttable, test], AppendTo[otable, h], Null];AppendTo[ttable, test];h++)];otable

Formula

Binary(a(n)) x A203074 = n, where x is the inner product and the binary vector is in ascending powers of 2 with infinite trailing zeros.