

A242244


Primes p such that both p^2 + 2 and p^2  2 are semiprimes.


2



11, 17, 53, 73, 79, 83, 97, 251, 269, 281, 379, 389, 433, 461, 601, 631, 691, 739, 827, 929, 947, 983, 1033, 1087, 1187, 1303, 1423, 1483, 1531, 1637, 1709, 1847, 1879, 2447, 2473, 2683, 2833, 2843, 3301, 3463, 3557, 3719, 3727, 3779, 3833, 3907, 3931, 4157
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OFFSET

1,1


COMMENTS

Primes p such that p^2 + 2 = 3q, where q is prime, and p^2  2 is semiprime.


LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..3670


EXAMPLE

a(1) = 11 is prime: 11^2 + 2 = 123 = 3 * 41 which is semiprime: 11^2  2 = 119 = 7 * 17 which is also semiprime.
a(2) = 17 is prime: 17^2 + 2 = 291 = 3 * 97 which is semiprime: 17^2  2 = 287 = 7 * 41 which is also semiprime.


MAPLE

with(numtheory):A242244:= proc()if isprime(x) and bigomega(x^2+2)=2 and bigomega(x^22)=2 then RETURN (x); fi; end: seq(A242244 (), x=1..5000);


MATHEMATICA

A242244 = {}; Do[p = Prime[n]; If[PrimeOmega[p^2 + 2] == 2 && PrimeOmega[p^2  2] == 2, AppendTo[A242244, p]], {n, 2000}]; A242244
Select[Prime[Range[600]], PrimeOmega[#^2+{2, 2}]=={2, 2}&] (* Harvey P. Dale, Apr 07 2018 *)


PROG

(PARI) is(n)=isprime(n) && isprime((n^2+2)\3) && bigomega(n^22)==2 \\ Charles R Greathouse IV, May 15 2014


CROSSREFS

Cf. A000040, A005383, A063643, A115395.
Sequence in context: A267772 A046122 A217064 * A228031 A324795 A250716
Adjacent sequences: A242241 A242242 A242243 * A242245 A242246 A242247


KEYWORD

nonn


AUTHOR

K. D. Bajpai, May 09 2014


STATUS

approved



