A192734 Smallest number having binary weight of 3 and n distinct prime factors.

7, 21, 273, 16401, 1048593, 4295032833, 1099512676353, 9007199256838145, 302231455185132270387201, 1208944266358702884257793, 1329227995784915872903807060297121793, 1393796574908163946347162983661240005427201

Offset: 1

Author

Johan Särnbratt, Jul 08 2011

Keywords

• nonn
• base

Comments

Written in binary, these numbers have exactly three 1 bits and the other bits are all 0's. This means that these numbers are of the sum of 1 plus two larger distinct powers of 2. - Alonso del Arte, Jul 08 2011

a(n) > A002110(n). [Reinhard Zumkeller, Jul 09 2011]

Sequence is not monotone: a(12) > a(13). [Charles R Greathouse IV, Jul 11 2011]

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..14

Crossrefs

Cf. A084468, A001221.

Programs

Haskell

a192734 n = head [x | x <- [2^u + 2^v + 1 | u <- [2..], v <- [1..u-1]],
                      a001221 x == n]
-- Reinhard Zumkeller, Jun 14 2015, Jul 09 2011

Mathematica

list = {7}; For[max = 1; n = 2, n < 120,
For[m = 0, m < n,
  tal = 2*(2^n + 2^m) + 1; num = PrimeNu[tal];
  If[num > max, AppendTo[list, tal]; max = num]
  , m++], n++] (* Sarnbratt *)
A084468 = Flatten[Table[2^m + 2^n + 1, {m, 2, 80}, {n, m - 1}]]; Flatten[Table[Take[Select[A084468, PrimeNu[#] == n &], 1], {n, 10}]] (* Alonso del Arte, Jul 08 2011 *)

PARI

a(n)={
  my(t);
  for(a=2,9e9,
    t=1+1<Charles R Greathouse IV, Jul 08 2011

Extensions

a(9) corrected by Charles R Greathouse IV, Jul 08 2011

a(12) from Charles R Greathouse IV, Jul 11 2011