A190944 Multiples of 3 written in base 2.

0, 11, 110, 1001, 1100, 1111, 10010, 10101, 11000, 11011, 11110, 100001, 100100, 100111, 101010, 101101, 110000, 110011, 110110, 111001, 111100, 111111, 1000010, 1000101, 1001000, 1001011, 1001110, 1010001, 1010100, 1010111, 1011010, 1011101, 1100000

Offset: 0

Author

N. J. A. Sloane, May 24 2011

Keywords

• nonn
• easy
• base

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000
• P. Flajolet et al., Mellin Transforms And Asymptotics: Digital Sums, Theoret. Computer Sci. 23 (1994), 291-314.
• D. J. Newman, On the number of binary digits in a multiple of three, Proc. Amer. Math. Soc. 21 (1969) 719-721.
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A002275, A002450, A007088, A008585, A036555.

Programs

Haskell

a190944 = a007088 . (* 3)  -- Reinhard Zumkeller, Sep 01 2013

Magma

[Seqint(Intseq(n, 2)): n in [0..90 by 3]];  // Bruno Berselli, May 25 2011

Maple

A190944 := proc(n) local b: if(n=0)then return 0: fi: b:=convert(3*n,base,2); return op(convert(b,base,10,10^nops(b))): end: seq(A190944(n),n=0..40); # Nathaniel Johnston, May 25 2011

Mathematica

FromDigits /@ IntegerDigits[Range[0, 99, 3], 2] (* Jean-François Alcover, May 09 2017 *)

PARI

a(n) = fromdigits(binary(3*n), 10); \\ Michel Marcus, Oct 25 2017

Formula

a(n) = A007088(A008585(n)). - Reinhard Zumkeller, Sep 01 2013

a(A002450(n)) = A002275(2n) = R_{2n}. - Bernard Schott, May 04 2021

Extensions

More terms from Bruno Berselli, May 25 2011