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Semiprimes whose binary representation, read in decimal, is prime.
1

%I #7 Jun 24 2014 11:39:39

%S 185,247,253,295,329,355,453,471,533,565,583,671,689,703,755,781,785,

%T 815,841,989,1037,1099,1121,1159,1189,1207,1219,1329,1403,1441,1473,

%U 1541,1555,1643,1661,1703,1751,1793,1797,1819,1821,1853,1921,1941,1957,2123,2189

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

%C Semiprimes in A036952.

%C Intersection of A001358 and A036952.

%H K. D. Bajpai, <a href="/A244248/b244248.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 185 = 5 * 37 which is semiprime. Binary representation of 185 = 10111001 which is prime.

%e a(2) = 247 = 13 * 19 which is semiprime. Binary representation of 247 = 11110111 which is prime.

%p with(numtheory):A244248 := proc() local a; a:=convert(n, binary); if bigomega(n)=2 and isprime(a) then RETURN (n) ; fi; end: seq(A244248 (), n=1..5000);

%t A244248={};Do[If[PrimeOmega[n]==2&&PrimeQ[FromDigits[IntegerDigits[n,2]]], AppendTo[A244248, n]], {n, 5000}]; A244248

%Y Cf. A000040, A001358, A036952, A242677.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jun 23 2014