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Odd semiprimes sandwiched by even semiprimes.
0

%I #11 Mar 03 2023 17:25:28

%S 9,25,33,35,39,77,85,95,141,155,201,259,355,361,395,481,559,565,623,

%T 763,799,841,865,879,923,933,979,1003,1043,1177,1199,1219,1227,1285,

%U 1293,1299,1437,1441,1517,1541,1603,1643,1655,1717,1769,1865,2005,2041,2095,2101,2123,2127,2183,2245

%N Odd semiprimes sandwiched by even semiprimes.

%C Odd semiprimes sp(k) = A001358(k) such that sp(k-1) and sp(k+1) are even. Values of k: 3, 9, 11, 13, 15, 26, 28, 34, 46, 51, 63, 83, 112, 114, 125, 148, 175, 177, 190, 230, 242, 253, 259, 264, 278, 280, 293.

%e a(1) = 9: A001358(2) = 6, A001358(3) = 9, A001358(4) = 10;

%e a(2) = 25: A001358(8) = 22, A001358(9) = 25, A001358(10) = 26.

%t s = Select[Range[2300], Plus @@ Last /@ FactorInteger[#] == 2 &]; Transpose[ Select[ Partition[s, 3, 1], Mod[#, 2] == {0, 1, 0} &]][[2]] (* _Giovanni Resta_, Jun 10 2018 *)

%t Module[{nn=2500,sp},sp=Select[Range[nn],PrimeOmega[#]==2&];Select[Partition[ sp,3,1],Mod[ #,2] =={0,1,0}&]][[;;,2]] (* _Harvey P. Dale_, Mar 03 2023 *)

%Y Cf. A001358.

%K nonn

%O 1,1

%A _Zak Seidov_, Jun 10 2018