login
Semiprimes whose binary representation, read in decimal, is also semiprime.
2

%I #7 May 21 2014 20:07:11

%S 15,33,55,57,65,69,77,87,115,121,129,143,169,205,209,265,299,305,321,

%T 339,361,415,417,447,451,481,493,505,517,519,535,551,553,581,611,623,

%U 667,687,695,721,737,779,789,799,865,871,893,901,905,923,943,949,955,973

%N Semiprimes whose binary representation, read in decimal, is also semiprime.

%H K. D. Bajpai, <a href="/A242677/b242677.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2) = 33 = 3 * 11 is semiprime. Binary representation of 33 = 100001 = 11 * 9091 which is also semiprime.

%e a(4) = 57 = 3 * 19 is semiprime. Binary representation of 57 = 111001 = 11 * 10091 which is also semiprime.

%p with(numtheory):A242677 := proc() if bigomega(n)=2 and bigomega(convert(n, binary))=2 then RETURN (n) ; fi; end: seq(A242677(), n=1..2000);

%t c = 0; Do[If [PrimeOmega[n] == 2 && PrimeOmega[FromDigits[IntegerDigits[n, 2]]] == 2, c ++; Print[c, " ", n]], {n, 1, 3*10^5}];

%Y Cf. A001358, A236365, A236537, A241764.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, May 20 2014