cp's OEIS Frontend

A223078 Positive integers with the property that if the base-4 representation is reversed the result is three times the original number.

%I A223078 #10 Apr 23 2019 23:53:06
%S A223078 75,315,1275,5115,19275,20475,76875,81915,307275,322875,327675,
%T A223078 1228875,1290555,1310715,4915275,4934475,5161275,5223675,5242875,
%U A223078 19660875,19741515,20644155,20890875,20971515,78643275,78720075,78969675,82575675,82652475,83559675
%N A223078 Positive integers with the property that if the base-4 representation is reversed the result is three times the original number.
%C A223078 From _Robert Israel_, Apr 23 2019: (Start)
%C A223078 All terms are divisible by 15.
%C A223078 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 A223078 Robert Israel, <a href="/A223078/b223078.txt">Table of n, a(n) for n = 1..985</a>
%p A223078 rev4:= proc(n) local L,i;
%p A223078   L:= convert(n,base,4);
%p A223078   add(L[-i]*4^(i-1),i=1..nops(L))
%p A223078 end proc:
%p A223078 Res:= NULL:
%p A223078 for d from 2 to 15 do
%p A223078   d1:= ceil(d/2); d2:= d-d1;
%p A223078   for a from 4^(d1-1) to 4^d1/3 do
%p A223078      b:= rev4(a)/3 mod 4^d2;
%p A223078      x:= 4^d2*a+b;
%p A223078      if rev4(x) = 3*x then Res:= Res, x; fi
%p A223078 od od:
%p A223078 Res; # _Robert Israel_, Apr 23 2019
%t A223078 Select[Range[84*10^6],3#==FromDigits[Reverse[IntegerDigits[#,4]],4]&] (* _Harvey P. Dale_, Mar 03 2018 *)
%Y A223078 Cf. A173951, A223077, A223079, A214927.
%K A223078 nonn,base
%O A223078 1,1
%A A223078 _N. J. A. Sloane_, Mar 14 2013
%E A223078 More terms from _Alois P. Heinz_, Mar 14 2013