A188059 Numbers k with the property that k, k+1 and 2*k+1 are all semiprimes.

25, 34, 38, 57, 93, 118, 133, 145, 177, 201, 205, 213, 218, 298, 334, 361, 381, 394, 446, 501, 633, 694, 698, 842, 865, 878, 898, 921, 1114, 1141, 1226, 1285, 1293, 1465, 1513, 1654, 1713, 1726, 1761, 1857, 1893, 1941, 1981, 2018, 2041, 2217, 2306, 2426, 2433, 2577, 2581, 2734, 2746, 2901, 2973, 3133, 3193, 3214, 3241, 3386, 3578, 3661, 3693, 3746, 3754, 3777, 3826, 3957

Offset: 1

Author

Zak Seidov, Mar 20 2011

Keywords

• nonn

Comments

Numbers k such that 2k+1 is a semiprime and the sum of two consecutive semiprimes (k and k+1).

Examples

			25 is a term: k = 25 = 5*5, k+1 = 26 = 2*13, 2k+1 = 51 = 3*17.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1309 (terms < 200000)

Crossrefs

Cf. A001358 (semiprimes).

Cf. A176896 (safe semiprimes), A111153 (Sophie Germain semiprimes), A070552.

Programs

Mathematica

Select[Range[4000],Union[PrimeOmega[{#,#+1,2 #+1}]]=={2}&] (* Harvey P. Dale, May 11 2012 *)

Formula

Equals A111153 intersect A070552. - M. F. Hasler, Mar 20 2011