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

Author

Reinhard Zumkeller, Jul 20 2003

Keywords

• nonn
• base
• look

Comments

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

Examples

			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.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Dario A. Alpern, Brilliant Numbers.

Crossrefs

Cf. A078972, A007088, A070939, A055642.

Cf. A084126, A084127, A070939.

Cf. A138510, A174956.

Cf. A261073, A261074, A261075 (subsequences).

Intersection of A001358 and A266346.

Programs

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

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 *)

PARI

is(n)=bigomega(n)==2&&#binary(factor(n)[1,1])==#binary(n/factor(n)[1,1]) \\ Charles R Greathouse IV, Nov 08 2011

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010