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A192734 Smallest number having binary weight of 3 and n distinct prime factors 1
7, 21, 273, 16401, 1048593, 4295032833, 1099512676353, 9007199256838145, 302231455185132270387201, 1208944266358702884257793, 1329227995784915872903807060297121793, 1393796574908163946347162983661240005427201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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 *)

PROG

(PARI) a(n)={

  my(t);

  for(a=2, 9e9,

    t=1+1<<a;

    for(b=1, a-1,

      if(omega(t+1<<b)==n, return(t+1<<b))

    )

  )

}; \\ Charles R Greathouse IV, Jul 08 2011

(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

CROSSREFS

Cf. A084468, A001221.

Sequence in context: A060146 A111878 A133279 * A220161 A213152 A082826

Adjacent sequences:  A192731 A192732 A192733 * A192735 A192736 A192737

KEYWORD

nonn,base

AUTHOR

Johan Särnbratt, 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

STATUS

approved

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Last modified June 19 03:38 EDT 2021. Contains 345125 sequences. (Running on oeis4.)