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A145351 Prime-indexed composites k such that lpf(k) + gpf(k) is a prime.

%I A145351 #17 May 18 2019 17:19:33
%S A145351 6,10,20,22,30,44,54,58,66,82,96,108,120,136,142,144,204,232,324,330,
%T A145351 340,352,384,464,492,544,596,616,704,738,750,792,870,894,918,960,990,
%U A145351 1062,1234,1312,1318,1326,1498,1534,1540,1566,1576,1632,1694,1700,1722
%N A145351 Prime-indexed composites k such that lpf(k) + gpf(k) is a prime.
%H A145351 Harvey P. Dale, <a href="/A145351/b145351.txt">Table of n, a(n) for n = 1..1000</a>
%e A145351 6 is a term because it is the 2nd composite number, 6=2*3, and 2+3=5 is prime;
%e A145351 10 is a term because it is the 5th composite number, 10=2*5, and 2+5=7 is prime;
%e A145351 22 is a term because it is the 13th composite number, 22=2*11, and 2+11=13 is prime;
%e A145351 44 is a term because it is the 29th composite number, 44=2*2*11, and 2+11=13 is prime.
%p A145351 A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
%p A145351 A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:
%p A145351 A002808 := proc(n) if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do: end if; end proc:
%p A145351 A065858 := proc(n) A002808(ithprime(n)) ; end proc:
%p A145351 A145351 := proc(n) c := A065858(n) ; if isprime(A020639(c) + A006530(c)) then printf("%d,",c) ; end if; end proc:
%p A145351 seq(A145351(n),n=1..400) ; # _R. J. Mathar_, May 01 2010
%t A145351 pfiQ[n_]:=Module[{f=FactorInteger[n]},PrimeQ[f[[1,1]]+f[[-1,1]]]]; Module[ {nn=2000,c},c=Select[ Range[nn],CompositeQ];Select[ Table[ Take[c,{n}][[1]],{n,Prime[Range[PrimePi[Length[c]]]]}],pfiQ]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 18 2019 *)
%Y A145351 Cf. A000040, A002808, A020639 (lpf), A006530 (gpf).
%K A145351 nonn
%O A145351 1,1
%A A145351 _Juri-Stepan Gerasimov_, Jan 04 2009
%E A145351 Corrected (inserted 20 from n=5, 30 from n=8, removed 200) and extended beyond 204 by _R. J. Mathar_, May 01 2010
%E A145351 Edited by _Jon E. Schoenfield_, Feb 07 2019