A055039 Numbers of the form 2^(2i+1)*(8j+7).

14, 30, 46, 56, 62, 78, 94, 110, 120, 126, 142, 158, 174, 184, 190, 206, 222, 224, 238, 248, 254, 270, 286, 302, 312, 318, 334, 350, 366, 376, 382, 398, 414, 430, 440, 446, 462, 478, 480, 494, 504, 510, 526, 542, 558, 568, 574, 590, 606, 622

Offset

1,1

Comments

The numbers not of the form x^2+y^2+2z^2.

These are the numbers not occurring as norms in the face-centered cubic lattice (cf. A004015).

Numbers whose base 4 representation ends in 3,2 followed by some number of zeros. - Franklin T. Adams-Watters, Dec 04 2006

Links

T. D. Noe, Table of n, a(n) for n=1..10000

L. E. Dickson, Integers represented by positive ternary quadratic forms, Bull. Amer. Math. Soc. 33 (1927), 63-70.

L. J. Mordell, A new Waring's problem with squares of linear forms, Quart. J. Math., 1 (1930), 276-288 (see p. 283).

Steve Waterman, Missing numbers formula

Formula

Consists of numbers of the form 6x^2 + 8x^2*(2y -1). (Steve Waterman).

Example

In base 4: 32, 132, 232, 320, 332, 1032, 1132, 1232, 1320, 1332, 2032,...

Prog

(Python)
from itertools import count, islice
def A055039_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:(m:=(~n&n-1).bit_length())&1 and (n>>m)&7==7, count(max(startvalue, 1)))
A055039_list = list(islice(A055039_gen(), 30)) # Chai Wah Wu, Jul 09 2022

Crossrefs

Equals twice A004215. Not the same as A044075 - see A124169.

Complement of A000401.

Sequence in context: A230720 A053751 A063311 * A044075 A044456 A132759

Adjacent sequences: A055036 A055037 A055038 * A055040 A055041 A055042

Keyword

nonn

Author

N. J. A. Sloane, Jun 01 2000

Status

approved