A037819 Number of i such that d(i)>d(i-1), where Sum{d(i)*4^i: i=0,1,....,m} is base 4 representation of n.

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0

Offset

1,36

Comments

From Jeffrey Shallit, May 15 2016: (Start)

A "2-regular" sequence, satisfying the recurrence relations:

a(4n+3) = a(n)

a(16n) = a(16n+1) = a(16n+2) = a(4n)

a(16n+5) = a(16n+6) = a(4n+1)

a(16n+8) = a(16n+9) = a(4n+2) + 1

a(16n+10) = a(4n+2)

a(16n+12) = a(16n+13) = a(16n+14) = a(4n+1) + 1

a(64n+4) = a(4n) + 1

a(64n+20) = a(16n+4)

a(64n+36) = a(4n+2) + 2

a(64n+52) = a(n) + 2

(End)

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Maple

A037819 := proc(n)
    a := 0 ;
    dgs := convert(n, base, 4);
    for i from 2 to nops(dgs) do
        if op(i, dgs)>op(i-1, dgs) then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Oct 15 2015

Mathematica

Table[Count[Differences@ IntegerDigits[n, 4], k_ /; k < 0], {n, 120}] (* Michael De Vlieger, May 15 2016 *)

Crossrefs

Cf. A037802.

Sequence in context: A325616 A056978 A321761 * A090405 A237837 A365126

Adjacent sequences: A037816 A037817 A037818 * A037820 A037821 A037822

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Sign in Name corrected by R. J. Mathar, Oct 15 2015

Status

approved