A089226 Smallest composite number with exactly n 1's in binary representation.

4, 6, 14, 15, 55, 63, 247, 255, 511, 1023, 2047, 4095, 12287, 16383, 32767, 65535, 196607, 262143, 983039, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 3221225471

Offset: 1

Author

Reinhard Zumkeller, Dec 10 2003

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..3318

Crossrefs

Cf. A000043, A000120, A000225, A023416, A061712.

Programs

Maple

f:= proc(n) local i,t;
  for i from n to 0 by -1 do
    t:= 2^(n+1) - 2^i - 1;
    if not isprime(t) then return t fi
  od
end proc:
f(1):= 4:
map(f, [$1..100]); # Robert Israel, Jun 20 2019

Mathematica

a[n_] := Module[{i, t},
  For[i = n, i >= 0, i--,
     t = 2^(n+1) - 2^i - 1;
     If[!PrimeQ[t], Return [t]]]];
a[1] = 4;
Array[a, 100] (* Jean-François Alcover, Dec 16 2021, after Robert Israel *)

Formula

A000120(a(n)) = n; A023416(a(n)) <= 1 for n>1. - Ray Chandler, Feb 15 2004

a(n) = A000225(n) unless n is in A000043. - Robert Israel, Jun 20 2019

Extensions

More terms from Ray Chandler, Feb 15 2004