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A055045
Numbers of the form 4^i*(8*j+5).
5
5, 13, 20, 21, 29, 37, 45, 52, 53, 61, 69, 77, 80, 84, 85, 93, 101, 109, 116, 117, 125, 133, 141, 148, 149, 157, 165, 173, 180, 181, 189, 197, 205, 208, 212, 213, 221, 229, 237, 244, 245, 253, 261, 269, 276, 277, 285, 293, 301, 308, 309, 317
OFFSET
1,1
COMMENTS
Numbers not of the form x^2+2y^2+6z^2.
LINKS
L. E. Dickson, Integers represented by positive ternary quadratic forms, Bull. Amer. Math. Soc. 33 (1927), 63-70. See Theorem XI.
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) = 6n + O(log n). - Charles R Greathouse IV, Dec 19 2013
PROG
(PARI) is(n)=n/=4^valuation(n, 4); n%8==5 \\ Charles R Greathouse IV and V. Raman, Dec 19 2013
(Haskell)
a055045 n = a055045_list !! (n-1)
a055045_list = filter ((== 5) . (flip mod 8) . f) [1..] where
f x = if r == 0 then f x' else x where (x', r) = divMod x 4
-- Reinhard Zumkeller, Jan 02 2014
(Python)
from itertools import count, islice
def A055045_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:not (m:=(~n&n-1).bit_length())&1 and (n>>m)&7==5, count(max(startvalue, 1)))
A055045_list = list(islice(A055045_gen(), 30)) # Chai Wah Wu, Jul 09 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 01 2000
STATUS
approved