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A201997 a(n) is the decimal value of the binary vector used to select terms of A075058 whose sum is n.

%I A201997 #29 Jun 22 2023 23:34:43
%S A201997 0,1,2,4,5,6,7,8,9,10,12,13,14,16,17,18,20,21,22,23,24,25,26,32,33,34,
%T A201997 36,37,38,39,40,41,42,44,45,46,48,49,50,52,53,54,55,56,57,58,60,64,65,
%U A201997 66,68,69,70,71,72,73,74,76,77,78,80,81,82,84,85,86,87
%N A201997 a(n) is the decimal value of the binary vector used to select terms of A075058 whose sum is n.
%H A201997 Wikipedia, <a href="http://en.wikipedia.org/wiki/Complete_sequence">"Complete" sequence</a>. [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]
%F A201997 Binary(a(n)) x A075058 = n, where x is the inner product and the binary vector is in ascending powers of 2 with infinite trailing zeros.
%e A201997 For n=22, the binary vector when applied to A075058 is {0,1,0,1,1,0,...}, consequently 2+7+13=22. The decimal value of the binary vector (in ascending powers of 2) is 26, so a(22)=26.
%t A201997 prevprime[n_Integer] := (j=n; If[n==1, 1, While[!PrimeQ[j], j--]; j]); aprime[n_Integer] := (aprime[n]=prevprime[Sum[aprime[m], {m, 0, n - 1}] + 1]); gentable[n_Integer] := (m=n; ptable={0}; While[m!=0, (i=0; While[aprime[i]<=m && ptable[[i + 1]]!=1, (AppendTo[ptable, 0];i++)]; ptable[[i]] = 1; m = m - aprime[i - 1])]; ptable); decimal[n_Integer] := (gentable[n]; Sum[2^(k-1)*ptable[[k]], {k, 1, Length[ptable]}]); aprime[0]=1; Table[decimal[r], {r,0,100}]
%Y A201997 Cf. A007924, A066352, A200947, A075058.
%K A201997 nonn,base,more
%O A201997 0,3
%A A201997 _Frank M Jackson_, Dec 07 2011
%E A201997 Edited by _N. J. A. Sloane_, May 20 2023