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

1,1

Comments

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

Subsequence of A228184.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A001358, A228183, A238242, A228184.

Sequence in context: A225120 A308250 A215056 * A341177 A117459 A137558

Adjacent sequences: A242699 A242700 A242701 * A242703 A242704 A242705

Keyword

nonn

Author

K. D. Bajpai, May 20 2014

Status

approved