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A037848 a(n)=Sum{d(i-1)-d(i): d(i) where Sum{d(i)*7^i: i=0,1,...,m} is the base 7 representation of n.

%I A037848 #11 Jan 19 2018 19:36:23
%S A037848 0,0,0,0,0,0,0,0,1,2,3,4,5,0,0,0,1,2,3,4,0,0,0,0,1,2,3,0,0,0,0,0,1,2,
%T A037848 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,2,3,4,5,6,0,0,1,2,3,4,5,1,1,1,2,3,4,
%U A037848 5,2,2,2,2,3,4,5,3,3,3,3,3,4,5,4,4,4,4,4,4,5
%N A037848 a(n)=Sum{d(i-1)-d(i): d(i)<d(i-1), i=1,...,m}, where Sum{d(i)*7^i: i=0,1,...,m} is the base 7 representation of n.
%C A037848 This is the base-7 up-variation sequence; see A297330. - _Clark Kimberling_, Jan 18 2017
%H A037848 Clark Kimberling, <a href="/A037848/b037848.txt">Table of n, a(n) for n = 1..10000</a>
%p A037848 A037848 := proc(n)
%p A037848     a := 0 ;
%p A037848     dgs := convert(n,base,7);
%p A037848     for i from 2 to nops(dgs) do
%p A037848         if op(i,dgs)<op(i-1,dgs) then
%p A037848             a := a-op(i,dgs)+op(i-1,dgs) ;
%p A037848         end if;
%p A037848     end do:
%p A037848     a ;
%p A037848 end proc: # _R. J. Mathar_, Oct 19 2015
%t A037848 g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 7; z = 120;
%t A037848 Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037857*)
%t A037848 Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037848*)
%Y A037848 Cf. A297330
%K A037848 nonn,base
%O A037848 1,10
%A A037848 _Clark Kimberling_
%E A037848 Definition swapped with A037857. - _R. J. Mathar_, Oct 19 2015
%E A037848 Updated by _Clark Kimberling_, Jan 19 2018