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

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

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

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

Adjacent sequences: A243362 A243363 A243364 * A243366 A243367 A243368

Keyword

nonn

Author

K. D. Bajpai, Jun 24 2014

Status

approved