A055050 Numbers of the form 4^i*(8*j+3) or 4^i*(8*j+7).

3, 7, 11, 12, 15, 19, 23, 27, 28, 31, 35, 39, 43, 44, 47, 48, 51, 55, 59, 60, 63, 67, 71, 75, 76, 79, 83, 87, 91, 92, 95, 99, 103, 107, 108, 111, 112, 115, 119, 123, 124, 127, 131, 135, 139, 140, 143, 147, 151, 155, 156, 159, 163, 167, 171, 172

Offset

1,1

Comments

The numbers not of the form x^2+y^2+4z^2.

Positions of 3 in A065882. - Clark Kimberling, Oct 19 2016

The asymptotic density of this sequence is 1/3. - Amiram Eldar, Mar 08 2021

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

M. A. Bennett and B. Reznick, Positive rational solutions to x^y = y^{mx}: : A Number-Theoretic Excursion, Amer. Math. Monthly, 111 (No. 1, 2004), 13-21.

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

Mathematica

t = Table[Mod[n/4^IntegerExponent[n, 4], 4], {n, 1, 160}] (*A065882*)
Flatten[Position[t, 3]] (*A055050*) (* Clark Kimberling, Oct 19 2016 *)

Crossrefs

Sequence in context: A310191 A135137 A263737 * A096346 A104534 A062823

Adjacent sequences: A055047 A055048 A055049 * A055051 A055052 A055053

Keyword

nonn

Author

N. J. A. Sloane, Jun 02 2000

Status

approved