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%I #18 Sep 08 2022 08:46:24
%S 61273,109441,160213,274501,275473,311593,360673,394201,477181,486061,
%T 514993,522085,617137,620053,715477,725485,803833,812677,847117,
%U 1063585,1146913,1182577,1215865,1232917,1409425,1508113,1587241,1768993,1863073,1895413,2085517,2095177
%N Numbers k such that k + 6^t is semiprime for t = 0 to 9.
%C a(2620) = 530079693 is the first multiple of 3 in this sequence; there are no multiples of 2. - _Charles R Greathouse IV_, Dec 20 2019
%H Charles R Greathouse IV, <a href="/A330508/b330508.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 61273:
%e 61273 + 6^0 = 61274 = 2 * 30637;
%e 61273 + 6^1 = 61279 = 233 * 263;
%e 61273 + 6^2 = 61309 = 37 * 1657;
%e 61273 + 6^3 = 61489 = 17 * 3617;
%e 61273 + 6^4 = 62569 = 13 * 4813;
%e 61273 + 6^5 = 69049 = 29 * 2381;
%e 61273 + 6^6 = 107929 = 37 * 2917;
%e 61273 + 6^7 = 341209 = 11 * 31019;
%e 61273 + 6^8 = 1740889 = 197 * 8837;
%e 61273 + 6^9 = 10138969 = 89 * 113921;
%e all ten results are semiprime.
%t fX[n_] = PrimeOmega[n] == 2; Select[Range[2000000], AllTrue[# + 6^{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, fX] &]
%o (Magma) f:=func<n|&+[d[2]: d in Factorization(n)] eq 2>; [k:k in [1..2100000]|forall{m:m in [0..9]|f(k+6^m)}]; // _Marius A. Burtea_, Dec 20 2019
%o (PARI) issemi(n)=bigomega(n)==2
%o is(n)=for(t=0,9, if(!issemi(n+6^t), return(0))); 1 \\ _Charles R Greathouse IV_, Dec 20 2019
%Y Subsequence of A076274.
%Y Cf. A001358, A082919, A096173, A104238, A105041.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Dec 16 2019
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