A176747 - OEIS

%I #15 Sep 26 2022 06:17:12

%S 0,1,3,5,6,10,14,15,21,23,28,32,36,40,45,52,55,66,74,78,82,86,91,105,

%T 113,117,120,124,136,153,155,166,171,184,190,197,201,209,210,217,228,

%U 231,247,253,276,278,300,311,325,349,351,378,390,406,435,439,465,474,496,516,518

%N Triangular numbers and numbers which cannot be represented as a sum of two earlier members of the sequence.

%e 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.

%e 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.

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

%p 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;

%p 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:

%p seq(A176747(n),n=0..60) ; # _R. J. Mathar_, Nov 01 2010

%p # Alternative:

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

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

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

%p for k from 0 to upto do

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

%p P end: print(A176747_list(518));  # _Peter Luschny_, Jul 20 2022

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

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

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

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

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

%t P];

%t A176747list[518] (* _Jean-François Alcover_, Sep 26 2022, after _Peter Luschny_ *)

%Y Cf. A000217, A176744, A176745, A176746.

%K nonn

%O 0,3

%A _Vladimir Shevelev_, Apr 25 2010

%E Definition rephrased, sequence extended beyond 55 by _R. J. Mathar_, Nov 01 2010