A115395 -id:A115395 - cp's OEIS frontend

A242244 Primes p such that both p^2 + 2 and p^2 - 2 are semiprimes.

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

Offset: 1

K. D. Bajpai, May 09 2014

nonn

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

			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.

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

Cf. A000040, A005383, A063643, A115395.

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

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 *)

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

A243365 Primes p such that both p^2 + 6 and p^2 - 6 are semiprime.

Original entry on oeis.org

101, 157, 173, 229, 233, 239, 347, 349, 353, 421, 439, 479, 521, 577, 619, 661, 719, 751, 761, 829, 881, 1019, 1061, 1117, 1129, 1153, 1277, 1289, 1321, 1447, 1453, 1489, 1523, 1579, 1721, 1733, 1801, 1811, 1823, 1831, 1861, 1871, 1873, 2027, 2099, 2221, 2239

Offset: 1

K. D. Bajpai, Jun 24 2014

nonn

			101 is in the sequence because 101 is prime. 101^2 + 6 = 10207 = 59 * 173 which is semiprime. 101^2 - 6 = 10195 = 5 * 2039 which is semiprime.
157 is in the sequence because 157 is prime. 157^2 + 6 = 24655 = 5 * 4931 which is semiprime. 157^2 - 6 = 24643 = 19 * 1297 which is semiprime.

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

Cf. A000040 (primes), A001358 (semiprimes).

Cf. A117328 (p+/-4 semiprime), A115395(p+/-6 semiprime), A242244 (p^2+/-2 semiprime).

with(numtheory): A243365:= proc()local k; k:=ithprime(n); if bigomega(k^2+6)=2 and bigomega(k^2-6)=2 then RETURN (k); fi; end: seq(A243365 (),n=1..5000);

A243365 = {}; k = Prime[n]; Do[If[PrimeOmega[k^2 + 6] == 2 && PrimeOmega[k^2 - 6] == 2, AppendTo[A243365, k]], {n, 1000}]; A243365
Select[Prime[Range[400]],PrimeOmega[#^2+{6,-6}]=={2,2}&] (* Harvey P. Dale, Jul 08 2014 *)

s=[]; forprime(p=2, 3000, if(bigomega(p^2+6)==2 && bigomega(p^2-6)==2, s=concat(s, p))); s \\ Colin Barker, Jun 25 2014

cp's OEIS Frontend

A242244 Primes p such that both p^2 + 2 and p^2 - 2 are semiprimes.

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