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

1,1

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A001358 (semiprimes).

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

Sequence in context: A020258 A227516 A281369 * A257720 A098368 A281370

Adjacent sequences: A188056 A188057 A188058 * A188060 A188061 A188062

Keyword

nonn

Author

Zak Seidov, Mar 20 2011

Status

approved