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Numbers k such that the k-th semiprime + 2 is prime.
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%I #10 Dec 01 2019 19:28:09

%S 3,6,7,13,15,18,20,23,24,26,30,34,36,43,51,54,57,68,75,78,80,86,91,98,

%T 99,106,108,116,117,118,119,125,128,132,135,138,150,151,153,154,161,

%U 171,185,186,187,192,201,204,207,212,215,217,221,223,226,228,232,233,237

%N Numbers k such that the k-th semiprime + 2 is prime.

%e 3 is a term because A001358(3) + 2 = 11 (prime);

%e 6 is a term because A001358(6) + 2 = 17 (prime).

%p isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:

%p A001358 := proc(n) option remember ; if n = 1 then return 4 ; else for a from procname(n-1)+1 do if isA001358(a) then return a; end if; end do; end if; end proc:

%p for n from 1 to 300 do if isprime( A001358(n)+2 ) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Apr 20 2010

%t Position[Select[Range[1000],PrimeOmega[#]==2&],_?(PrimeQ[#+2]&)]//Flatten (* _Harvey P. Dale_, Dec 01 2019 *)

%Y Cf. A001358 (semiprimes).

%Y Cf. A176065.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Apr 14 2010

%E Entries checked by _R. J. Mathar_, Apr 20 2010