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A243365
Primes p such that both p^2 + 6 and p^2 - 6 are semiprime.
2
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
1,1
LINKS
EXAMPLE
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.
MAPLE
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);
MATHEMATICA
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 *)
PROG
(PARI) 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
CROSSREFS
Cf. A000040 (primes), A001358 (semiprimes).
Cf. A117328 (p+/-4 semiprime), A115395(p+/-6 semiprime), A242244 (p^2+/-2 semiprime).
Sequence in context: A243890 A129563 A141927 * A107186 A142660 A123037
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Jun 24 2014
STATUS
approved