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

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

Author

N. J. A. Sloane, Mar 14 2013

Keywords

• nonn
• base

Comments

From Robert Israel, Apr 23 2019: (Start)

All terms are divisible by 15.

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

Links

• Robert Israel, Table of n, a(n) for n = 1..985

Crossrefs

Cf. A173951, A223077, A223079, A214927.

Programs

Maple

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

Mathematica

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

Extensions

More terms from Alois P. Heinz, Mar 14 2013