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A297142
Numbers whose base-8 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}.
5
1, 2, 3, 4, 5, 6, 7, 9, 18, 27, 36, 45, 54, 63, 64, 72, 73, 74, 75, 76, 77, 78, 79, 82, 91, 100, 109, 118, 127, 128, 137, 144, 145, 146, 147, 148, 149, 150, 151, 155, 164, 173, 182, 191, 192, 201, 210, 216, 217, 218, 219, 220, 221, 222, 223, 228, 237, 246
OFFSET
1,2
COMMENTS
These numbers comprise the complement of the set of numbers in the union of A297140 and A297141.
Differs from A044819 first for 513 = 1001_8, which has two consecutive equal digits and is in this sequence, but has two runs of equal length (1), and is not in A044819. - R. J. Mathar, Jan 17 2018
EXAMPLE
Base-8 digits of 5000: 1,1,6,1,0, so that 5000 is in the sequence.
MAPLE
read("transforms") :
isA297142 := proc(n)
local dgs, ud;
dgs := convert(n, base, 8) ;
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 isA297142(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 = 8; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297140 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &] (* A297141 *)
Complement[Range[z], Union[u, v]] (* A297142 *)
CROSSREFS
Sequence in context: A039126 A083376 A044957 * A044819 A048305 A043711
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Jan 15 2018
STATUS
approved