A297139 Numbers whose base-7 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, 8, 16, 24, 32, 40, 48, 49, 56, 57, 58, 59, 60, 61, 62, 65, 73, 81, 89, 97, 98, 106, 112, 113, 114, 115, 116, 117, 118, 122, 130, 138, 146, 147, 155, 163, 168, 169, 170, 171, 172, 173, 174, 179, 187, 195, 196, 204, 212, 220, 224, 225, 226

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 A297137 and A297138.

Differs from A044818 first for 344 = 1001_7. 1001_7 has two runs of length 1 and is not in A044818, but it has a sequence of two consecutive zeros and is in this sequence. - R. J. Mathar, Jan 18 2018

Examples

			Base-7 digits of 4998: 2,0,4,0,0, so that 4998 is in the sequence.
		

Crossrefs

Cf. A297137, A297138.

Programs

Maple

read("transforms") :
isA297139 := proc(n)
        local dgs,ud;
        dgs := convert(n,base,7) ;
        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 isA297139(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 = 7; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297137 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297138 *)
Complement[Range[z], Union[u, v]]  (* A297139 *)