A217837 Numbers n such that 4n - 1 and 4n + 1 are both semiprimes.

14, 23, 30, 36, 40, 46, 51, 54, 55, 59, 62, 72, 75, 76, 80, 82, 85, 98, 103, 104, 113, 118, 129, 132, 134, 136, 138, 145, 167, 170, 172, 174, 195, 198, 204, 225, 240, 264, 270, 275, 280, 284, 285, 287, 292, 301, 314, 318, 329, 336, 337, 339, 346, 347, 348

Offset: 1

Author

Zak Seidov, Oct 12 2012

Keywords

• nonn

Comments

This is to semiprimes as A045753 is to primes.

Examples

			a(1) = 14 because 56 - 1 = 5*11 and 56 + 1 = 3*19 are semiprimes, and this is the first number having this property.
a(2) = 23 because 92 - 1 = 7*13 and 92 + 1 = 3*31 are semiprimes, and this is the second number having this property.
a(3) = 30 because 120 - 1 = 7*17 and 120 + 1 = 11*11 are semiprimes, and this is the third number having this property.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A045753.

Programs

Mathematica

Select[Range[500], PrimeOmega[4# - 1] == 2 && PrimeOmega[4# + 1] == 2 &] (* Alonso del Arte, Oct 12 2012 *)