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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.
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%I #14 Jul 31 2024 09:14:03

%S 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,

%T 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,

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

%N 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.

%C This is the base-6 total variation sequence; see A297330. - _Clark Kimberling_, Jan 18 2017

%H Clark Kimberling, <a href="/A037838/b037838.txt">Table of n, a(n) for n = 1..10000</a>

%p A037838 := proc(n)

%p local dgs ;

%p dgs := convert(n,base,6);

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

%p end proc:

%p seq(A037838(n),n=1..100) ; # _R. J. Mathar_, Jul 31 2024

%t b = 6; 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 1,9

%A _Clark Kimberling_

%E Updated by _Clark Kimberling_, Jan 20 2018