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A297142
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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}.
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5
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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Base-8 digits of 5000: 1,1,6,1,0, so that 5000 is in the sequence.
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MAPLE
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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;
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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