A244248 Semiprimes whose binary representation, read in decimal, is prime.

185, 247, 253, 295, 329, 355, 453, 471, 533, 565, 583, 671, 689, 703, 755, 781, 785, 815, 841, 989, 1037, 1099, 1121, 1159, 1189, 1207, 1219, 1329, 1403, 1441, 1473, 1541, 1555, 1643, 1661, 1703, 1751, 1793, 1797, 1819, 1821, 1853, 1921, 1941, 1957, 2123, 2189

Offset: 1

Author

K. D. Bajpai, Jun 23 2014

Keywords

• nonn
• base

Comments

Semiprimes in A036952.

Intersection of A001358 and A036952.

Examples

			a(1) = 185 = 5 * 37 which is semiprime. Binary representation of 185 = 10111001 which is prime.
a(2) = 247 = 13 * 19 which is semiprime. Binary representation of 247 = 11110111 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001358, A036952, A242677.

Programs

Maple

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);

Mathematica

A244248={};Do[If[PrimeOmega[n]==2&&PrimeQ[FromDigits[IntegerDigits[n,2]]], AppendTo[A244248, n]], {n, 5000}]; A244248
Select[Range[2500],PrimeOmega[#]==2&&PrimeQ[FromDigits[IntegerDigits[#,2]]]&] (* Harvey P. Dale, Jun 22 2025 *)