A176744 The squares A000290 and the integers which cannot be represented as a sum of two earlier terms of the sequence.

0, 1, 3, 4, 9, 11, 16, 21, 23, 25, 31, 33, 36, 38, 43, 49, 51, 64, 77, 81, 83, 91, 96, 100, 118, 121, 135, 144, 150, 163, 169, 176, 189, 196, 203, 211, 213, 223, 225, 230, 237, 243, 256, 278, 283, 289, 291, 315, 324, 350, 361, 390, 395, 400, 408, 430, 437, 441, 484, 497, 510

Offset: 0

Author

Vladimir Shevelev, Apr 25 2010

Keywords

• nonn
• easy

Examples

			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.
		

Crossrefs

Cf. A000290.

Programs

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 *)

Extensions

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