A223077
Positive integers, written in base 3, with the property that if the base-3 representation is reversed the result is twice the original number.
Original entry on oeis.org
1012, 10212, 102212, 1022212, 10121012, 10222212, 101201012, 102222212, 1012001012, 1021210212, 1022222212, 10120001012, 10212010212, 10222222212, 101200001012, 101210121012, 102120010212, 102212102212, 102222222212, 1012000001012, 1012102121012, 1021200010212, 1022120102212, 1022222222212
Offset: 1
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b3rQ[n_]:=FromDigits[Reverse[IntegerDigits[n]],3]/FromDigits[ IntegerDigits[ n],3] ==2; Select[FromDigits/@Tuples[{0,1,2},13],b3rQ]//Quiet (* Harvey P. Dale, Jun 10 2018 *)
A173952
a(1)=32 and, for n > 1, a(n) = 9*a(n-1) + 32.
Original entry on oeis.org
32, 320, 2912, 26240, 236192, 2125760, 19131872, 172186880, 1549681952, 13947137600, 125524238432, 1129718145920, 10167463313312, 91507169819840, 823564528378592, 7412080755407360, 66708726798666272, 600378541187996480
Offset: 1
A223078
Positive integers with the property that if the base-4 representation is reversed the result is three times the original number.
Original entry on oeis.org
75, 315, 1275, 5115, 19275, 20475, 76875, 81915, 307275, 322875, 327675, 1228875, 1290555, 1310715, 4915275, 4934475, 5161275, 5223675, 5242875, 19660875, 19741515, 20644155, 20890875, 20971515, 78643275, 78720075, 78969675, 82575675, 82652475, 83559675
Offset: 1
-
rev4:= proc(n) local L,i;
L:= convert(n,base,4);
add(L[-i]*4^(i-1),i=1..nops(L))
end proc:
Res:= NULL:
for d from 2 to 15 do
d1:= ceil(d/2); d2:= d-d1;
for a from 4^(d1-1) to 4^d1/3 do
b:= rev4(a)/3 mod 4^d2;
x:= 4^d2*a+b;
if rev4(x) = 3*x then Res:= Res, x; fi
od od:
Res; # Robert Israel, Apr 23 2019
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Select[Range[84*10^6],3#==FromDigits[Reverse[IntegerDigits[#,4]],4]&] (* Harvey P. Dale, Mar 03 2018 *)
A223079
Positive integers, written in base 4, with the property that if the base-4 representation is reversed the result is three times the original number.
Original entry on oeis.org
1023, 10323, 103323, 1033323, 10231023, 10333323, 102301023, 103333323, 1023001023, 1032310323, 1033333323, 10230001023, 10323010323, 10333333323, 102300001023, 102310231023, 103230010323, 103323103323, 103333333323
Offset: 1
Showing 1-4 of 4 results.
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