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

0,3

Links

Table of n, a(n) for n=0..60.

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

Cf. A000290.

Sequence in context: A091380 A321871 A050006 * A023420 A004657 A054075

Adjacent sequences: A176741 A176742 A176743 * A176745 A176746 A176747

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