A055049 Numbers of the form 5^(2*i+1)*(5*j+-2).

10, 15, 35, 40, 60, 65, 85, 90, 110, 115, 135, 140, 160, 165, 185, 190, 210, 215, 235, 240, 250, 260, 265, 285, 290, 310, 315, 335, 340, 360, 365, 375, 385, 390, 410, 415, 435, 440, 460, 465, 485, 490, 510, 515, 535, 540, 560, 565, 585, 590

Offset

1,1

Comments

The numbers not of the form x^2+2y^2+5z^2.

Links

David A. Corneth, 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).

Formula

a(n) ~ 12 * n. - David A. Corneth, Apr 12 2015

Example

a(19) = a(1) + 25 * floor((19 - 1)/2) = 235 - David A. Corneth, Mar 31 2015

Maple

N:= 1000: # to get all terms <= N
A:= {}:
for i from 0 to floor((log[5](N)-1)/2) do
   a:= 5^(2*i+1);
   A:= A union {seq(a*(5*j+2), j=0..floor((N/a-2)/5))}
      union {seq(a*(5*j-2), j=1..floor((N/a+2)/5))};
od:
A; # if using Maple 11 or earlier, uncomment the next line
# sort(convert(A, list)); # Robert Israel, Apr 13 2015

Mathematica

Take[ Union@ Flatten@ Table[ 5^(2i + 1) (j), {i, 0, 1}, {j, Select[ Range@ 120, Mod[#, 5] == 2 || Mod[#, 5] == 3 &] }], 50] (* Robert G. Wilson v, Mar 30 2015 *)

Prog

(PARI) is(n) = v=valuation(n, 5); r=(n/5^v)%5; v%2==1&&(r==2||r==3) \\ David A. Corneth, Apr 12 2015

Crossrefs

Sequence in context: A060535 A239595 A037379 * A128703 A276914 A078818

Adjacent sequences: A055046 A055047 A055048 * A055050 A055051 A055052

Keyword

nonn

Author

N. J. A. Sloane, Jun 02 2000

Status

approved