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A179502 Numbers k with the property that k^2, k^2+1 and k^2+2 are all semiprimes.

%I A179502 #25 May 12 2025 11:46:23
%S A179502 11,29,79,271,379,461,521,631,739,881,929,1459,1531,1709,2161,2239,
%T A179502 2341,2729,3049,3491,3709,4021,4349,4561,4691,5021,5281,5851,5879,
%U A179502 6301,6329,6829,7559,8009,9151,10069,10099,10151,10529,10891,11719,11959,11969,13799,14051,14159
%N A179502 Numbers k with the property that k^2, k^2+1 and k^2+2 are all semiprimes.
%C A179502 From the first 10^6 primes, 6680 are terms of the sequence.
%C A179502 Also, all numbers k^2+1 are twice prime, and k^2+2 are thrice prime.
%C A179502 The number of terms less than 10^m beginning with m = 1: 0, 3, 11, 35, 160, 759, 4668, 30319, 204439, ..., .
%C A179502 The number of terms less than the (10^m)-th prime beginning with m = 1: 2, 7, 33, 165, 941, 6680, 48977, 373627, ..., .
%H A179502 Zak Seidov, <a href="/A179502/b179502.txt">Table of n, a(n) for n = 1..6680</a>
%t A179502 fQ[n_] := PrimeQ[(n^2 + 1)/2] && PrimeQ[(n^2 + 2)/3]; Select[ Prime@ Range@ 1667, fQ] (* _Robert G. Wilson v_, Feb 26 2011 *)
%t A179502 Select[Range[15000],PrimeOmega[#^2+{0,1,2}]=={2,2,2}&] (* _Harvey P. Dale_, May 12 2025 *)
%o A179502 (PARI){n=10;for(i=1,10^4,n=nextprime(n+1);n2=n^2;if(2==bigomega(n2+1)&&2==bigomega(n2+2),print1(n,",")))}
%Y A179502 n^2 are squares in A070552, which is a subsequence of A056809 (m and m+1 are semiprimes) and A001358 (semiprimes).
%Y A179502 The sequence is a subsequence of A048161.
%K A179502 nonn
%O A179502 1,1
%A A179502 _Zak Seidov_, Jan 08 2011