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%I #12 Sep 08 2022 08:46:15
%S 12,53,84,204,207,251,379,413,456,471,483,631,687,705,765,783,1079,
%T 1135,1140,1167,1269,1335,1347,1395,1475,1515,1587,1641,1709,1767,
%U 1851,1855,1943,1959,2049,2157,2319,2325,2575,2843,2865,3099,3153,3225,3267,3601,3779
%N Numbers n such that n^2 + 2, n^2 - 2, n + 2 and n - 2 are all semiprimes.
%H K. D. Bajpai, <a href="/A268186/b268186.txt">Table of n, a(n) for n = 1..3379</a>
%e 12 appears in the sequence because:
%e 12^2 + 2 = 146 = 2*73
%e 12^2 - 2 = 142 = 2*71
%e 12 + 2 = 14 = 2*7
%e 12 - 2 = 10 = 2*5 are all semiprimes.
%p with(numtheory): select(n -> (bigomega(n^2 + 2)=2 and bigomega(n^2 - 2)=2 and bigomega(n + 2)=2 and bigomega(n - 2)=2), [seq(n, n=1..10000)]);
%t Select[Range[10000], PrimeOmega[#^2 + 2] == PrimeOmega[#^2 - 2] == PrimeOmega[# + 2] == PrimeOmega[# - 2] == 2 &]
%o (PARI) for(n = 1, 10000,if(bigomega(n^2 + 2) == 2 && bigomega(n^2 - 2) == 2 && bigomega(n + 2) == 2 && bigomega(n - 2) == 2, print1(n, ", ")))
%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>;[ n : n in [2..10000] | IsSemiprime(n^2 + 2) and IsSemiprime(n^2 - 2) and IsSemiprime(n + 2) and IsSemiprime(n - 2)];
%Y Subsequence of A105571.
%Y Cf. A001358, A086005, A096173, A096175, A105571, A124936, A237037, A268043.
%K nonn,less
%O 1,1
%A _K. D. Bajpai_, Jan 28 2016
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