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A176747 Triangular numbers and numbers which cannot be represented as a sum of two earlier members of the sequence. 6
0, 1, 3, 5, 6, 10, 14, 15, 21, 23, 28, 32, 36, 40, 45, 52, 55, 66, 74, 78, 82, 86, 91, 105, 113, 117, 120, 124, 136, 153, 155, 166, 171, 184, 190, 197, 201, 209, 210, 217, 228, 231, 247, 253, 276, 278, 300, 311, 325, 349, 351, 378, 390, 406, 435, 439, 465, 474, 496, 516, 518 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

EXAMPLE

5 is the smallest number which is not represented as sum of 2 numbers of the set {0,1,3}. Therefore 5 is in the sequence.

14 is the smallest number which is not represented as sum of 2 numbers of the set {0,1,3,5,6,10}. Therefore 14 is in the sequence.

MAPLE

isA000217 := proc(n) issqr(8*n+1) ; end proc:

A176747 := proc(n) option remember; if n <=1 then n; else for a from procname(n-1)+1 do if isA000217(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(A176747(n), n=0..60) ; # R. J. Mathar, Nov 01 2010

# Alternative:

A176747_list := proc(upto) local P, k, issum, istri; P := [];

issum := k -> ormap(p -> member(k - p, P), P);

istri := k -> issqr(8*k + 1);

for k from 0 to upto do

    if istri(k) or not issum(k) then P := [op(P), k] fi od;

P end: print(A176747_list(518));  # Peter Luschny, Jul 20 2022

MATHEMATICA

A176747list[upto_] := Module[{P = {}, issum, istri},

issum[k_] := AnyTrue[P, MemberQ[P, k-#]&];

istri[k_] := IntegerQ@Sqrt[8k+1];

For[k = 0, k <= upto, k++,

   If[istri[k] || !issum[k], AppendTo[P, k]]];

P];

A176747list[518] (* Jean-Fran├žois Alcover, Sep 26 2022, after Peter Luschny *)

CROSSREFS

Cf. A000217, A176744, A176745, A176746.

Sequence in context: A115823 A190721 A112926 * A238488 A230124 A027627

Adjacent sequences:  A176744 A176745 A176746 * A176748 A176749 A176750

KEYWORD

nonn,changed

AUTHOR

Vladimir Shevelev, Apr 25 2010

EXTENSIONS

Definition rephrased, sequence extended beyond 55 by R. J. Mathar, Nov 01 2010

STATUS

approved

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Last modified October 6 23:36 EDT 2022. Contains 357270 sequences. (Running on oeis4.)