A055052 - OEIS

A055052

Numbers of the form 4^i*(8j+7) or 4^i*(8j+5).

5, 7, 13, 15, 20, 21, 23, 28, 29, 31, 37, 39, 45, 47, 52, 53, 55, 60, 61, 63, 69, 71, 77, 79, 80, 84, 85, 87, 92, 93, 95, 101, 103, 109, 111, 112, 116, 117, 119, 124, 125, 127, 133, 135, 141, 143, 148, 149, 151, 156, 157, 159, 165, 167, 173, 175

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OFFSET

1,1

COMMENTS

Numbers not of the form x^2+2y^2+8z^2.

The integers that are ratios between the terms constitute the sequence's complement within A003159. - Peter Munn, Feb 07 2024

The asymptotic density of this sequence is 1/3. - Amiram Eldar, Feb 09 2024

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

MATHEMATICA

Select[Range[200], MemberQ[{5, 7}, Mod[# / 4^IntegerExponent[#, 4], 8]] &] (* Amiram Eldar, Feb 09 2024 *)

CROSSREFS

Disjoint union of A004215 and A055045.

Subsequence of A003159, A097700.

Sequence in context: A314313 A339921 A066980 * A314314 A314315 A047550

Adjacent sequences: A055049 A055050 A055051 * A055053 A055054 A055055

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 02 2000

STATUS

approved