A176744 - OEIS

%I #14 Aug 02 2022 09:18:35

%S 0,1,3,4,9,11,16,21,23,25,31,33,36,38,43,49,51,64,77,81,83,91,96,100,

%T 118,121,135,144,150,163,169,176,189,196,203,211,213,223,225,230,237,

%U 243,256,278,283,289,291,315,324,350,361,390,395,400,408,430,437,441,484,497,510

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

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

%e 4 is a square, and included as such.

%e 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.

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

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

%p 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:

%p end if; end proc: seq(A176744(n),n=0..60) ; # _R. J. Mathar_, Oct 29 2010

%t 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]]]]]];

%t Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Aug 02 2022 *)

%Y Cf. A000290.

%K nonn,easy

%O 0,3

%A _Vladimir Shevelev_, Apr 25 2010

%E Definition rephrased, more examples added, and sequence extended beyond 51 by _R. J. Mathar_, Oct 29 2010