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
Keywords
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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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);
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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 *)
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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