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A014133 Sum of a square and a triangular number.

%I A014133 #15 Jul 08 2025 02:52:53
%S A014133 0,1,2,3,4,5,6,7,9,10,11,12,14,15,16,17,19,21,22,24,25,26,28,29,30,31,
%T A014133 32,35,36,37,39,40,42,44,45,46,49,50,51,52,53,54,55,56,57,59,61,64,65,
%U A014133 66,67,70,71,72,74,75,77,78,79,80,81,82,84,85,87,91
%N A014133 Sum of a square and a triangular number.
%H A014133 Harvey P. Dale, <a href="/A014133/b014133.txt">Table of n, a(n) for n = 0..1000</a>
%F A014133 {k: A101428(k) > 0} .- _R. J. Mathar_, Apr 28 2020
%p A014133 isA014133 := proc(n)
%p A014133     local c,t ;
%p A014133     for c from 0 do
%p A014133         t := c*(c+1)/2 ;
%p A014133         if t > n then
%p A014133             return false;
%p A014133         end if;
%p A014133         if issqr(n-t) then
%p A014133             return true;
%p A014133         end if;
%p A014133     end do:
%p A014133 end proc:
%p A014133 for n from 0 to 100 do
%p A014133     if isA014133(n) then
%p A014133         printf("%d,",n) ;
%p A014133     end if;
%p A014133 end do: # _R. J. Mathar_, Oct 11 2014
%t A014133 With[{nn=20},Select[Union[Flatten[Outer[Plus,Range[0,nn]^2,Accumulate[ Range[ 0,nn]]]]], #<=(nn(nn+1))/2&]] (* _Harvey P. Dale_, Dec 29 2019 *)
%Y A014133 Cf. A014134 (complement).
%K A014133 nonn
%O A014133 0,3
%A A014133 _N. J. A. Sloane_