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A176744
The squares A000290 and the integers which cannot be represented as a sum of two earlier terms of the sequence.
8
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
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 A376654 A004657
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