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

8, 13, 18, 20, 23, 27, 33, 34, 38, 41, 43, 47, 48, 58, 60, 62, 63, 68, 69, 73, 76, 83, 86, 88, 89, 90, 93, 97, 98, 99, 108, 111, 112, 113, 118, 123, 125, 132, 133, 134, 135, 138, 139, 143, 146, 148, 151, 158, 160, 163, 164, 167, 168, 173, 174

Offset

1,1

Comments

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

Links

R. J. Mathar, Table of n, a(n) for n = 1..4646

Maple

N:= 1000: # to generate all terms <= N
{$1 .. N} minus {seq(seq(x*(x+1)/2 + y^2, y = 0 .. floor(sqrt(N - x*(x+1)/2))),
x = 0 .. floor((sqrt(8*N+1)-1)/2))};
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%, list)); # Robert Israel, Mar 17 2015

Mathematica

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 *)

Prog

(PARI) is_A014134(n)=for(k=0, sqrtint(n*2), issquare(n-k*(k+1)/2)&return); 1 /* M. F. Hasler, Jan 05 2009 */

Crossrefs

Cf. A140867.

Sequence in context: A204221 A348277 A337308 * A085989 A319879 A095097

Adjacent sequences: A014131 A014132 A014133 * A014135 A014136 A014137

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved