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A037860
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Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*10^i: i=0,1,...,m} is base 10 representation of n.
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4
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 9
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OFFSET
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1,20
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COMMENTS
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This is the base-10 down-variation sequence; see A297330.
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LINKS
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MAPLE
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a := 0 ;
dgs := convert(n, base, 10);
for i from 2 to nops(dgs) do
if op(i, dgs)>op(i-1, dgs) then
a := a+op(i, dgs)-op(i-1, dgs) ;
end if;
end do:
a ;
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MATHEMATICA
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g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 10; z = 120;
Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}]; (*A037860*)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (*A037851*)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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