A085721 Semiprimes whose prime factors have an equal number of digits in binary representation.

4, 6, 9, 25, 35, 49, 121, 143, 169, 289, 323, 361, 391, 437, 493, 527, 529, 551, 589, 667, 713, 841, 899, 961, 1369, 1517, 1591, 1681, 1739, 1763, 1849, 1927, 1961, 2021, 2173, 2183, 2209, 2257, 2279, 2419, 2491, 2501, 2537, 2623, 2773, 2809

Offset

1,1

Comments

A138510(A174956(a(n))) <= 2. - Reinhard Zumkeller, Dec 19 2014

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Dario A. Alpern, Brilliant Numbers.

Example

A078972(35) = 527 = 17*31 -> 10001*11111, therefore 527 is a term;
A078972(37) = 533 = 13*41 -> 1101*101001, therefore 533 is not a term;
A001358(1920) = 7169 = 67*107 -> 1000011*1101011: therefore 7169 a term, but not of A078972.

Mathematica

fQ[n_] := Block[{fi = FactorInteger@ n}, Plus @@ Last /@ fi == 2 && IntegerLength[ fi[[1, 1]], 2] == IntegerLength[ fi[[-1, 1]], 2]]; Select[ Range@ 2866, fQ] (* Robert G. Wilson v, Oct 29 2011 *)
Select[Range@ 3000, And[Length@ # == 2, IntegerLength[#1, 2] == IntegerLength[#2, 2] & @@ #] &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ #] &] (* Michael De Vlieger, Oct 08 2016 *)

Prog

(PARI) is(n)=bigomega(n)==2&&#binary(factor(n)[1, 1])==#binary(n/factor(n)[1, 1]) \\ Charles R Greathouse IV, Nov 08 2011
(Haskell)
a085721 n = a085721_list !! (n-1)
a085721_list = [p*q | (p, q) <- zip a084126_list a084127_list,
                      a070939 p == a070939 q]
-- Reinhard Zumkeller, Nov 10 2013

Crossrefs

Cf. A078972, A007088, A070939, A055642.

Cf. A084126, A084127, A070939.

Cf. A138510, A174956.

Cf. A261073, A261074, A261075 (subsequences).

Intersection of A001358 and A266346.

Sequence in context: A246569 A368648 A326063 * A190300 A338378 A081614

Adjacent sequences: A085718 A085719 A085720 * A085722 A085723 A085724

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Jul 20 2003

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

Status

approved