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

CROSSREFS

Cf. A140867.

Sequence in context: A178968 A006613 A204221 * A085989 A095097 A187227

Adjacent sequences:  A014131 A014132 A014133 * A014135 A014136 A014137

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 4 02:25 EST 2016. Contains 278745 sequences.