A192321 Semiprime numbers n such that n^2 + n + 1 is prime.

6, 14, 15, 21, 33, 38, 57, 62, 69, 77, 111, 119, 141, 143, 155, 161, 194, 203, 206, 209, 215, 218, 278, 287, 309, 314, 329, 381, 395, 398, 447, 453, 489, 533, 537, 551, 554, 566, 579, 626, 635, 671, 755, 785, 818, 878, 899, 959, 974, 993, 1007, 1011, 1041, 1067, 1077, 1133, 1142, 1149, 1191, 1202, 1263

Offset: 1

Author

Jonathan Vos Post, Dec 19 2012

Keywords

• nonn
• easy

Examples

			309 is in the sequence because 309 is semiprime (309 = 3 * 103) and 309^2 + 309 + 1 = 95791 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A182253 and A001358.

Subsequence of A182253.

Programs

Mathematica

Select[Range[2000],PrimeOmega[#]==2&&PrimeQ[#^2+#+1]&] (* Harvey P. Dale, Feb 26 2013 *)

PARI

issemi(n)=bigomega(n)==2
is(n)=isprime(n^2+n+1) && issemi(n) \\ Charles R Greathouse IV, Jun 13 2017