A098971 a(0)=1; for n > 0, a(n)=a(floor(n/2))+2*a(floor(n/4)).

1, 3, 5, 5, 11, 11, 11, 11, 21, 21, 21, 21, 21, 21, 21, 21, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 171, 171, 171, 171, 171

Offset: 0

Author

Benoit Cloitre, Oct 23 2004

Keywords

• nonn

Crossrefs

a(2^n) gives the Jacobsthal sequence A001045(n+3).

Cf. A001045, A007731.

Programs

PARI

a(n)=if(n<1,1,(1/3)*(8*2^(floor(log(n)/log(2)))+(-1)^(floor(log(n)/log(2)))))

Python

def A098971(n): return ((1<<(m:=n.bit_length()+2))+(1 if m&1 else -1))//3 # Chai Wah Wu, Oct 10 2024

Formula

n>0, a(n) = (1/3)*(8*2^(floor(log(n)/log(2)))+(-1)^(floor(log(n)/log(2)))).