

A242702


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



