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A203076
Convert A203075(n) to base 10.
2
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
0,3
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]
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.
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
CROSSREFS
Sequence in context: A119024 A321453 A374038 * A247180 A375398 A317091
KEYWORD
nonn
AUTHOR
STATUS
approved