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

1,1

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

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 *)

Crossrefs

Cf. A173951, A223077, A223079, A214927.

Sequence in context: A292313 A158765 A226741 * A055561 A350245 A193252

Adjacent sequences: A223075 A223076 A223077 * A223079 A223080 A223081

Keyword

nonn,base

Author

N. J. A. Sloane, Mar 14 2013

Extensions

More terms from Alois P. Heinz, Mar 14 2013

Status

approved