

A014134


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


8



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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(nk*(k+1)/2)&return); 1 /* M. F. Hasler, Jan 05 2009 */


CROSSREFS

Cf. A140867.
Sequence in context: A006613 A204221 A337308 * A085989 A319879 A095097
Adjacent sequences: A014131 A014132 A014133 * A014135 A014136 A014137


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



