A223078 - OEIS

%I #10 Apr 23 2019 23:53:06

%S 75,315,1275,5115,19275,20475,76875,81915,307275,322875,327675,

%T 1228875,1290555,1310715,4915275,4934475,5161275,5223675,5242875,

%U 19660875,19741515,20644155,20890875,20971515,78643275,78720075,78969675,82575675,82652475,83559675

%N Positive integers with the property that if the base-4 representation is reversed the result is three times the original number.

%C From _Robert Israel_, Apr 23 2019: (Start)

%C All terms are divisible by 15.

%C If x is a term and x < 4^k, then x*(4^k+1) is a term.  In particular the sequence is infinite. (End)

%H Robert Israel, <a href="/A223078/b223078.txt">Table of n, a(n) for n = 1..985</a>

%p rev4:= proc(n) local L,i;

%p   L:= convert(n,base,4);

%p   add(L[-i]*4^(i-1),i=1..nops(L))

%p end proc:

%p Res:= NULL:

%p for d from 2 to 15 do

%p   d1:= ceil(d/2); d2:= d-d1;

%p   for a from 4^(d1-1) to 4^d1/3 do

%p      b:= rev4(a)/3 mod 4^d2;

%p      x:= 4^d2*a+b;

%p      if rev4(x) = 3*x then Res:= Res, x; fi

%p od od:

%p Res; # _Robert Israel_, Apr 23 2019

%t Select[Range[84*10^6],3#==FromDigits[Reverse[IntegerDigits[#,4]],4]&] (* _Harvey P. Dale_, Mar 03 2018 *)

%Y Cf. A173951, A223077, A223079, A214927.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, Mar 14 2013

%E More terms from _Alois P. Heinz_, Mar 14 2013