A037851 a(n)=Sum{d(i-1)-d(i): d(i)<d(i-1), i=1,...,m}, where Sum{d(i)*10^i: i=0,1,...,m} is the base 10 representation of n.

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

Offset

1,13

Comments

This is the base-10 up-variation sequence; see A297330.

Links

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

Maple

A037851 := proc(n)
    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 ;
end proc: # R. J. Mathar, Oct 19 2015

Mathematica

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*)

Crossrefs

Cf. A297330, A037860.

Sequence in context: A265540 A075011 A283001 * A037887 A207505 A235049

Adjacent sequences: A037848 A037849 A037850 * A037852 A037853 A037854

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Definition swapped with A037860. - R. J. Mathar, Oct 19 2015

Updated by Clark Kimberling, Jan 19 2018

Status

approved