A069024 Numbers that are palindromic in base 2 as well as in base 10 (initial zeros may be prepended).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 33, 40, 60, 66, 80, 90, 99, 252, 272, 292, 313, 330, 585, 626, 660, 717, 990, 2112, 2720, 2772, 2920, 4224, 5850, 6336, 7447, 7470, 8448, 8580, 9009, 15351, 21120, 22122, 25752, 32223, 39993, 40904, 42240, 44244, 48384

Offset: 1

Author

Amarnath Murthy, Apr 02 2002

Keywords

• nonn
• base

Examples

			66 in base 2 is 1000010, which is palindromic if rewritten as 01000010.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..243

Crossrefs

Cf. A007632.

Intersection of A061917 and A057890.

Programs

Maple

nextpal:= proc(p,d,V,b)
  local i,i2,pp,m,m2;
  pp:=p;
  V[1]:= V[1]+1;
  m2:= floor(d/2);
  i2:= ceil(d/2);
  if d::odd then pp:= pp + b^m2 else pp:= pp + b^m2 + b^(m2-1) fi;
  for i from 1 while V[i] = b do
    V[i]:= 0:
    if i = i2 then
      if d::even then
        ArrayTools:-Extend(V,[1],inplace);
        return b^d+1, d+1, V
      else
        V[i2]:= 1;
        return b^d+1, d+1, V;
      fi;
    fi;
    V[i+1]:= V[i+1]+1;
    if (d::odd and i=1) then pp:= pp + b^(i2-i-1) else
      pp:= pp + b^(i2-i-1) - b^(i2-i+1) fi;
  od;
  return pp, d, V
end proc:
count:= 1:
S:= 0:
p2[0]:=1: V2[0]:= <1>: d2[0]:= 1:m2:= 0:
p10[0]:= 1: V10[0]:= <1>: d10[0]:= 1: m10:= 0:
while count < 100 do
  i2:= min[index]([seq(p2[i],i=0..m2)])-1; p2o:= p2[i2];
  i10:= min[index]([seq(p10[i],i=0..m10)])-1; p10o:= p10[i10];
  if p2o = p10o then
    S:= S, p2o; count:= count+1;
  fi;
  if p2o <= p10o then x, d2[i2], V2[i2]:= nextpal(p2o/2^i2, d2[i2], V2[i2],2); p2[i2]:= 2^i2 *x;
    if i2 = m2 then m2:= m2+1; p2[m2]:= 2^m2; V2[m2]:= <1>; d2[m2]:= 1;
 fi;
  else
    x, d10[i10], V10[i10]:= nextpal(p10o/10^i10, d10[i10], V10[i10],10);
    p10[i10]:= 10^i10 * x;
    if i10 = m10 then m10:= m10+1; p10[m10]:= 10^m10; V10[m10]:= <1>; d10[m10]:= 1
fi fi od:
S; # Robert Israel, Apr 01 2024

Mathematica

pal[n_, b_] := (z=IntegerDigits[n, b]) == Reverse[z]; extpal[n_, b_] := If[Mod[n, b]>0, pal[n, b], extpal[n/b, b]]; Select[Range[50000], extpal[ #, 10]&&extpal[ #, 2]&]

Extensions

Edited by Dean Hickerson, Apr 06 2002

0 inserted by Sean A. Irvine, Mar 29 2024