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

1,1

Links

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

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

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 *)

Crossrefs

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

Sequence in context: A305842 A094298 A338045 * A102029 A310618 A310619

Adjacent sequences: A089223 A089224 A089225 * A089227 A089228 A089229

Keyword

nonn,base

Author

Reinhard Zumkeller, Dec 10 2003

Extensions

More terms from Ray Chandler, Feb 15 2004

Status

approved