A277549 Numbers k such that k/4^m == 1 (mod 4), where 4^m is the greatest power of 4 that divides k.

1, 4, 5, 9, 13, 16, 17, 20, 21, 25, 29, 33, 36, 37, 41, 45, 49, 52, 53, 57, 61, 64, 65, 68, 69, 73, 77, 80, 81, 84, 85, 89, 93, 97, 100, 101, 105, 109, 113, 116, 117, 121, 125, 129, 132, 133, 137, 141, 144, 145, 148, 149, 153, 157, 161, 164, 165, 169, 173

Offset

1,2

Comments

Positions of 1 in A065882.

This is one sequence in a 3-way splitting of the positive integers; the other two are A036554 and A055050, as in the Mathematica program.

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

Index entries for 2-automatic sequences.

Maple

filter:= n -> n/2^(2*floor(padic:-ordp(n, 2)/2)) mod 4 = 1:
select(filter, [$1..1000]); # Robert Israel, Oct 20 2016

Mathematica

z = 160; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}];
p[b_, d_] := Flatten[Position[a[b], d]];
p[4, 1] (* A277549 *)
p[4, 2] (* A036554 *)
p[4, 3] (* A055050 *)

Prog

(PARI) isok(n) = n/4^valuation(n, 4) % 4 == 1; \\ Michel Marcus, Oct 20 2016
(Python)
from itertools import count, islice
def A277549_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:(n>>((~n&n-1).bit_length()&-2))&3==1, count(max(startvalue, 1)))
A277549_list = list(islice(A277549_gen(), 30)) # Chai Wah Wu, Jul 09 2022

Crossrefs

Cf. A065882, A036554, A055050.

Sequence in context: A034705 A006844 A022425 * A331531 A363319 A363267

Adjacent sequences: A277546 A277547 A277548 * A277550 A277551 A277552

Keyword

nonn,easy

Author

Clark Kimberling, Oct 20 2016

Status

approved