A037836 - OEIS

%I #14 Jan 20 2018 12:37:54

%S 0,0,0,1,0,1,2,2,1,0,1,3,2,1,0,1,2,3,4,1,0,1,2,3,2,1,2,5,4,3,2,2,3,4,

%T 5,2,1,2,3,2,1,0,1,4,3,2,1,3,4,5,6,3,2,3,4,3,2,1,2,3,2,1,0,1,2,3,4,3,

%U 2,3,4,5,4,3,4,7,6,5,4,1,2,3,4,1,0,1,2,3,2,1

%N a(n) = Sum{|d(i)-d(i-1)|: i=1,...,m}, where Sum{d(i)*4^i: i=0,1,...,m} is the base 4 representation of n.

%C This is the base-4 total variation sequence; see A297330. - _Clark Kimberling_, Jan 18 2017

%H Clark Kimberling, <a href="/A037836/b037836.txt">Table of n, a(n) for n = 1..10000</a>

%p A037836 := proc(n)

%p     local dgs ;

%p     dgs := convert(n,base,4);

%p     add( abs(op(i,dgs)-op(i-1,dgs)),i=2..nops(dgs)) ;

%p end proc: # _R. J. Mathar_, Oct 16 2015

%t b = 4; z = 120; t = Table[Total@Flatten@Map[Abs@Differences@# &, Partition[IntegerDigits[n, b], 2, 1]], {n, z}] (* cf. _Michael De Vlieger_, A037834 *)

%Y Cf. A297330.

%K nonn,base

%O 1,7

%A _Clark Kimberling_

%E Updated by _Clark Kimberling_, Jan 20 2018