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
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
Programs
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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);
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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 *)
Comments