A242702 Semiprimes n such that n^2+n+41 is also semiprime.

49, 65, 82, 87, 91, 121, 122, 123, 143, 155, 159, 161, 178, 185, 187, 201, 205, 209, 213, 215, 217, 218, 237, 249, 259, 265, 278, 287, 289, 291, 295, 298, 299, 301, 302, 309, 314, 321, 326, 327, 329, 334, 361, 381, 395, 407, 422, 427, 445, 451, 454, 466, 471

Offset: 1

Author

K. D. Bajpai, May 20 2014

Keywords

• nonn

Comments

n^2+n+41 is sometimes referred to as Euler's polynomial.

Subsequence of A228184.

Examples

			65 = 5 * 13 is semiprime and 65^2 + 65 + 41 = 4331 = 61 * 71 is also semiprime so 65 is in the sequence.
87 = 3 * 29 is semiprime and 87^2 + 87 + 41 = 7697 = 43 * 179 is also semiprime so 87 is in the sequence.
6 = 2 * 3 is semiprime but 6^2+6+41 = 83 is prime (not semiprime) so 6 is not in the sequence.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A228183, A238242, A228184.

Programs

Maple

with(numtheory): A242702:= proc();  if bigomega(n)=2 and bigomega(n^2+n+41)=2 then RETURN (n); fi; end: seq(A242702 (), n=1..1000);

Mathematica

c = 0; Do[If [PrimeOmega[n] == 2 && PrimeOmega[n^2 + n + 41] == 2, c++; Print[c, "  ", n]], {n, 1, 10^5}];
Select[Range[500],PrimeOmega[#]==PrimeOmega[#^2+#+41]==2&] (* Harvey P. Dale, Nov 07 2016 *)