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A330508 Numbers k such that k + 6^t is semiprime for t = 0 to 9.

%I A330508 #18 Sep 08 2022 08:46:24
%S A330508 61273,109441,160213,274501,275473,311593,360673,394201,477181,486061,
%T A330508 514993,522085,617137,620053,715477,725485,803833,812677,847117,
%U A330508 1063585,1146913,1182577,1215865,1232917,1409425,1508113,1587241,1768993,1863073,1895413,2085517,2095177
%N A330508 Numbers k such that k + 6^t is semiprime for t = 0 to 9.
%C A330508 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 A330508 Charles R Greathouse IV, <a href="/A330508/b330508.txt">Table of n, a(n) for n = 1..10000</a>
%e A330508 a(1) = 61273:
%e A330508   61273 + 6^0  =    61274 =   2 *  30637;
%e A330508   61273 + 6^1  =    61279 = 233 *    263;
%e A330508   61273 + 6^2  =    61309 =  37 *   1657;
%e A330508   61273 + 6^3  =    61489 =  17 *   3617;
%e A330508   61273 + 6^4  =    62569 =  13 *   4813;
%e A330508   61273 + 6^5  =    69049 =  29 *   2381;
%e A330508   61273 + 6^6  =   107929 =  37 *   2917;
%e A330508   61273 + 6^7  =   341209 =  11 *  31019;
%e A330508   61273 + 6^8  =  1740889 = 197 *   8837;
%e A330508   61273 + 6^9  = 10138969 =  89 * 113921;
%e A330508 all ten results are semiprime.
%t A330508 fX[n_] = PrimeOmega[n] == 2; Select[Range[2000000], AllTrue[# + 6^{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, fX] &]
%o A330508 (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 A330508 (PARI) issemi(n)=bigomega(n)==2
%o A330508 is(n)=for(t=0,9, if(!issemi(n+6^t), return(0))); 1 \\ _Charles R Greathouse IV_, Dec 20 2019
%Y A330508 Subsequence of A076274.
%Y A330508 Cf. A001358, A082919, A096173, A104238, A105041.
%K A330508 nonn
%O A330508 1,1
%A A330508 _K. D. Bajpai_, Dec 16 2019