A037838 a(n) = Sum{|d(i)-d(i-1)|: i=1,...,m}, where Sum{d(i)*6^i: i=0,1,...,m} is the base 6 representation of n.

0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 4, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 1, 2, 4, 3, 2, 1, 0, 1, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 1, 0, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 3, 4, 7, 6, 5, 4, 3, 4, 9, 8, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7, 2, 1, 2, 3, 4, 5, 2, 1, 0, 1, 2, 3, 4

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

This is the base-6 total variation sequence; see A297330. - Clark Kimberling, Jan 18 2017

Links

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

Crossrefs

Cf. A297330.

Programs

Maple

A037838 := proc(n)
    local dgs ;
    dgs := convert(n,base,6);
    add( abs(op(i,dgs)-op(i-1,dgs)),i=2..nops(dgs)) ;
end proc:
seq(A037838(n),n=1..100) ; # R. J. Mathar, Jul 31 2024

Mathematica

b = 6; z = 120; t = Table[Total@Flatten@Map[Abs@Differences@# &, Partition[IntegerDigits[n, b], 2, 1]], {n, z}] (* cf. Michael De Vlieger, A037834 *)

Extensions

Updated by Clark Kimberling, Jan 20 2018