OFFSET

0,3

EXAMPLE

3 is the smallest number which is not a sum of 2 numbers of {0,1}. Therefore 3 in the sequence.

4 is a square, and included as such.

5 can be represented by 1+4 (both already in the sequence) and is not included; 6=3+3, 7=3+4, 8=4+4 are also sums of earlier terms: not included.

11 is the smallest number which is not a sum of 2 numbers of {0, 1, 3, 4, 9}. Therefore 11 in the sequence.

MAPLE

A176744 := proc(n) option remember; if n <=1 then n; else for a from procname(n-1)+1 do

if issqr(a) then return a; end if; isrep := false; for i from 1 to n-1 do for j from i to n-1 do if procname(i)+procname(j) = a then isrep := true; end if; end do: end do: if not isrep then return a; end if; end do:

end if; end proc: seq(A176744(n), n=0..60) ; # R. J. Mathar, Oct 29 2010

MATHEMATICA

a[n_] := a[n] = Module[{tt, k}, If[n == 0, 0, tt = Total /@ Tuples[Array[a, n-1], {2}]; For[k = a[n-1]+1, True, k++, If[IntegerQ@Sqrt@k, Return[k], If[FreeQ[tt, k], Return[k]]]]]];

Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Aug 02 2022 *)

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Vladimir Shevelev, Apr 25 2010

EXTENSIONS

Definition rephrased, more examples added, and sequence extended beyond 51 by R. J. Mathar, Oct 29 2010

STATUS

approved