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A176804 Lesser of twin primes p such that p = semiprime(k)/2 and p + 2 = semiprime(k+2)/2 for some integer k.

%I A176804 #14 Sep 24 2022 18:55:54
%S A176804 3,11,17,41,179,197,239,281,311,419,431,461,521,599,641,821,827,857,
%T A176804 1019,1049,1061,1091,1151,1229,1289,1319,1427,1481,1487,1607,1667,
%U A176804 1697,1721,1871,1877,1931,1997,2027,2081,2111,2141,2309,2339,2591,2687,2789
%N A176804 Lesser of twin primes p such that p = semiprime(k)/2 and p + 2 = semiprime(k+2)/2 for some integer k.
%H A176804 Harvey P. Dale, <a href="/A176804/b176804.txt">Table of n, a(n) for n = 1..1000</a>
%e A176804 3 is a term because 3 = semiprime(2)/2 = 6/2 and 3 + 2 = 5 = semiprime(2+2)/2 = 10/2.
%p A176804 From _R. J. Mathar_, Apr 27 2010: (Start)
%p A176804 isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
%p A176804 A001358 := proc(n) option remember ; if n = 1 then 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 A176804 A174956 := proc(p) for n from 1 do if A001358(n) = p then return n; elif A001358(n) > p then return 0 ; end if; end do: end proc:
%p A176804 A001359 := proc(n) option remember; if n = 1 then 3; else for a from procname(n-1)+2 by 2 do if isprime(a) and isprime(a+2) then return a; end if; end do: end if; end proc:
%p A176804 for i from 1 to 400 do p := A001359(i) ; n := A174956(2*p) ; n2 := A174956(2*p+4) ; if n > 0 and n2 >0 and n2=n+2 then printf("%d,",p) ; end if; end do: (End)
%t A176804 (Select[Partition[Select[Range[6000],PrimeOmega[#]==2&],3,1],AllTrue[ {#[[1]]/2 ,#[[3]]/2},PrimeQ]&&#[[3]]-#[[1]]==4&]/2)[[All,1]] (* _Harvey P. Dale_, Sep 24 2022 *)
%K A176804 nonn
%O A176804 1,1
%A A176804 _Juri-Stepan Gerasimov_, Apr 26 2010
%E A176804 Corrected (541 replaced by 521, 1047 replaced by 1049, 1741 replaced by 1721) by _R. J. Mathar_, Apr 27 2010