A097262 Numbers whose set of base 16 digits is {0,F}, where F base 16 = 15 base 10.

0, 15, 240, 255, 3840, 3855, 4080, 4095, 61440, 61455, 61680, 61695, 65280, 65295, 65520, 65535, 983040, 983055, 983280, 983295, 986880, 986895, 987120, 987135, 1044480, 1044495, 1044720, 1044735, 1048320, 1048335, 1048560, 1048575

Offset: 0

Author

Ray Chandler, Aug 03 2004

Keywords

• nonn
• base

Comments

n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a power of 16 for every i.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001196, A005823, A097251-A097261.

Programs

Magma

[n: n in [0..1110000] | Set(IntegerToSequence(n, 16)) subset {0, 15}]; // Vincenzo Librandi, Jun 05 2012

Mathematica

f[n_] := FromDigits[ IntegerDigits[n, 2] /. {1 -> 15}, 16]; Array[f, 32, 0] (* or *)
FromDigits[#, 16] & /@ Tuples[{0, 15}, 6] (* Harvey P. Dale, Sep 22 2011 *) (* or much slower *)
fQ[n_] := Union@ Join[{0, 15}, IntegerDigits[n, 16]] == {0, 15}; Select[ Range[0, 11000000 ], fQ] (* Robert G. Wilson v, May 12 2012 *)

Formula

a(n) = 15*A033052(n).

a(2n) = 16*a(n), a(2n+1) = a(2n)+15.