A297145 Numbers whose base-9 digits d(m), d(m-1), ..., d(0) have m=0 or else d(i) = d(i+1) for some i in {0,1,...,m-1}.

1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 60, 70, 80, 81, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 111, 121, 131, 141, 151, 161, 162, 172, 180, 181, 182, 183, 184, 185, 186, 187, 188, 192, 202, 212, 222, 232, 242, 243, 253, 263, 270, 271, 272, 273, 274

Offset: 1

Author

Clark Kimberling, Jan 15 2018

Keywords

• nonn
• easy
• base

Comments

These numbers comprise the complement of the set of numbers in the union of A297142 and A297143.

Differs from A044820 first for 730 = 1001_9, which is in this sequence but not in A044820. - R. J. Mathar, Jan 18 2018

Examples

			Base-9 digits of 9993: 1,4,6,3,3, so that 9993 is in the sequence.
		

Crossrefs

Cf. A297143, A297144.

Programs

Maple

read("transforms") :
isA297145 := proc(n)
    local dgs,ud;
    dgs := convert(n,base,9) ;
    if nops(dgs) < 2 then
        return true;
    end if;
    if 0 in DIFF(dgs) then
        true;
    else
        false;
    end if;
end proc:
for n from 1 to 300 do
    if isA297145(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jan 18 2018

Mathematica

a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 9; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297143 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297144 *)
Complement[Range[z], Union[u, v]]  (* A297145 *)