A036556 Integers which when multiplied by 3 have an odd number of 1's in their binary expansion (cf. A000069).

7, 14, 23, 27, 28, 29, 31, 39, 46, 54, 56, 57, 58, 62, 71, 78, 87, 91, 92, 93, 95, 103, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 119, 123, 124, 125, 127, 135, 142, 151, 155, 156, 157, 159, 167, 174, 182, 184, 185, 186, 190, 199, 206, 214

Offset: 1

Author

Dan Hoey

Keywords

• nonn
• base

Comments

In other words, numbers n such that 3n is odious.

Numbers n such that valuation(binomial(3n,n),2) is odd. - Benoit Cloitre, Jun 06 2004

Intersection of A000069 and A008585 (multiples of 3), divided by 3.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000069, A036555, A036557, A180963.

Programs

Magma

[ n : n in [0..150] | IsOdd(&+Intseq(3*n, 2))]; // Vincenzo Librandi, Apr 13 2011

Mathematica

Select[ Range[ 214 ], OddQ[ Plus@@IntegerDigits[ 3#, 2 ]]& ]

PARI

for(n=1,214,if(valuation(binomial(3*n,n),2)%2==1,print1(n,","))) \\ Benoit Cloitre, Jun 06 2004

Formula

a(n) = A180963(n)/3. - Amiram Eldar, Aug 06 2023

Extensions

Definition corrected by N. J. A. Sloane, Jan 09 2007