A037857 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*7^i: i=0,1,...,m} is base 7 representation of n.

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

Offset

1,14

Comments

This is the base-7 down-variation sequence; see A297330. - Clark Kimberling, Jan 18 2017

Links

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

Maple

A037857 := proc(n)
    a := 0 ;
    dgs := convert(n, base, 7);
    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 = 7; z = 120;
Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037857*)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037848*)

Crossrefs

Sequence in context: A173677 A219480 A277627 * A037875 A057764 A010108

Adjacent sequences: A037854 A037855 A037856 * A037858 A037859 A037860

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Definition swapped with A037848. - R. J. Mathar, Oct 19 2015

Updated by Clark Kimberling, Jan 19 2018

Status

approved