A037836 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.

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

Offset

1,7

Comments

This is the base-4 total variation sequence; see A297330. - Clark Kimberling, Jan 18 2017

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Maple

A037836 := proc(n)
    local dgs ;
    dgs := convert(n, base, 4);
    add( abs(op(i, dgs)-op(i-1, dgs)), i=2..nops(dgs)) ;
end proc: # R. J. Mathar, Oct 16 2015

Mathematica

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

Crossrefs

Cf. A297330.

Sequence in context: A109246 A037890 A037898 * A194522 A165013 A351995

Adjacent sequences: A037833 A037834 A037835 * A037837 A037838 A037839

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Updated by Clark Kimberling, Jan 20 2018

Status

approved