A200947 Sequence A007924 expressed in decimal.

0, 1, 2, 4, 5, 8, 9, 16, 17, 18, 20, 32, 33, 64, 65, 66, 68, 128, 129, 256, 257, 258, 260, 512, 513, 514, 516, 517, 520, 1024, 1025, 2048, 2049, 2050, 2052, 2053, 2056, 4096, 4097, 4098, 4100, 8192, 8193, 16384, 16385, 16386, 16388, 32768, 32769, 32770

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

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

a(n) = decimal(A007924(n)).

a(n) mod 2 = A121559(n) for n>=1. - Alois P. Heinz, Jun 12 2023

Example

8=7+1, hence A007924(8)=10001, so a(8)=17.

Maple

a:= proc(n) option remember; local m, p, r; m:=n; r:=0;
      while m>0 do
        if m=1 then r:=r+1; break fi;
        p:= prevprime(m+1); m:= m-p;
        r:= r+2^numtheory[pi](p)
      od; r
    end:
seq(a(n), n=0..52);  # Alois P. Heinz, Jun 12 2023

Mathematica

cprime[n_Integer] := If[n==0, 1, Prime[n]]; gentable[n_Integer] := (m=n; ptable={}; While[m != 0, (i = 0; While[cprime[i] <= m, i++]; j=0; While[j<i, AppendTo[ptable, 0]; j++]; ptable[[i]]=1; m=m-cprime[i-1])]; ptable); decimal[n_Integer] := (gentable[n]; Sum[2^(k - 1)*ptable[[k]], {k, 1, Length[ptable]}]); Table[decimal[n], {n, 0, 100}]

Crossrefs

Cf. A003714, A007895, A007924, A027941, A066352, A121559, A345297.

Sequence in context: A305076 A332223 A269361 * A350356 A333256 A227369

Adjacent sequences: A200944 A200945 A200946 * A200948 A200949 A200950

Keyword

nonn

Author

Frank M Jackson, Nov 24 2011

Extensions

Edited by N. J. A. Sloane, May 20 2023

Status

approved