cp's OEIS Frontend

A014134 Numbers that are not the sum of a square (A000290) and a triangular number (A000217).

%I A014134 #20 Dec 02 2015 11:58:12
%S A014134 8,13,18,20,23,27,33,34,38,41,43,47,48,58,60,62,63,68,69,73,76,83,86,
%T A014134 88,89,90,93,97,98,99,108,111,112,113,118,123,125,132,133,134,135,138,
%U A014134 139,143,146,148,151,158,160,163,164,167,168,173,174
%N A014134 Numbers that are not the sum of a square (A000290) and a triangular number (A000217).
%C A014134 n is in the sequence if for some prime p == 5 or 7 (mod 8), 8*n+1 is divisible by p but not by p^2. The first member of the sequence that does not have this property is 16078. - _Robert Israel_, Mar 17 2015
%H A014134 R. J. Mathar, <a href="/A014134/b014134.txt">Table of n, a(n) for n = 1..4646</a>
%p A014134 N:= 1000: # to generate all terms <= N
%p A014134 {$1 .. N} minus {seq(seq(x*(x+1)/2 + y^2, y = 0 .. floor(sqrt(N - x*(x+1)/2))),
%p A014134 x = 0 .. floor((sqrt(8*N+1)-1)/2))};
%p A014134 # if using Maple 11 or earlier, uncomment the next line
%p A014134 # sort(convert(%,list)); # _Robert Israel_, Mar 17 2015
%t A014134 fQ[n_] := Block[{k = 0, lmt = 1 + Floor@ Sqrt@ n}, While[k < lmt && !IntegerQ@ Sqrt[ 8(n - k^2) + 1], k++]; k == lmt]; Select[ Range@ 175, fQ@# &] (* _Robert G. Wilson v_, Nov 29 2015 *)
%o A014134 (PARI) is_A014134(n)=for(k=0,sqrtint(n*2),issquare(n-k*(k+1)/2)&return);1 /* _M. F. Hasler_, Jan 05 2009 */
%Y A014134 Cf. A140867.
%K A014134 nonn,easy
%O A014134 1,1
%A A014134 _N. J. A. Sloane_