A215883 When written in base 4, n ends in a(n) consecutive nonzero digits.

0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 1, 1, 0, 3, 3, 3, 0, 3, 3, 3, 0, 3, 3, 3, 0, 1, 1, 1, 0, 3, 3, 3, 0, 3, 3, 3, 0, 3, 3, 3, 0, 1, 1, 1, 0, 3, 3, 3, 0, 3, 3, 3, 0, 3, 3, 3, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 1, 1, 0, 4, 4

Offset: 0

Author

M. F. Hasler, Aug 25 2012

Keywords

• nonn
• base

Comments

Sequences A215879, A215884 and A215887 are the base 3, 5 and 10 analog, while the base 2 analog of this sequence coincides (up to a shift in the index) with the 2-adic valuation A007814, see comments there.

Examples

			The numbers 0,1,2,3,4,5,6,7 are written in base 4 as 0,1,2,3,10,11,12,13 and thus end in a(0..7)=0,1,1,1,0,2,2,2 nonzero digits.
		

Programs

PARI

a(n,b=4)=n=divrem(n,b); for(c=0,9e9,n[2]||return(c); n=divrem(n[1],b))

PARI

a(n)=my(k);while(n%4,n>>=2;k++);k \\ Charles R Greathouse IV, Sep 26 2013

Formula

a(4^(t+1)*k+m) = t for 4^t > m > 4^(t-1).