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A145351 Prime-indexed composites k such that lpf(k) + gpf(k) is a prime. 1

%I

%S 6,10,20,22,30,44,54,58,66,82,96,108,120,136,142,144,204,232,324,330,

%T 340,352,384,464,492,544,596,616,704,738,750,792,870,894,918,960,990,

%U 1062,1234,1312,1318,1326,1498,1534,1540,1566,1576,1632,1694,1700,1722

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

%H Harvey P. Dale, <a href="/A145351/b145351.txt">Table of n, a(n) for n = 1..1000</a>

%e 6 is a term because it is the 2nd composite number, 6=2*3, and 2+3=5 is prime;

%e 10 is a term because it is the 5th composite number, 10=2*5, and 2+5=7 is prime;

%e 22 is a term because it is the 13th composite number, 22=2*11, and 2+11=13 is prime;

%e 44 is a term because it is the 29th composite number, 44=2*2*11, and 2+11=13 is prime.

%p A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:

%p A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:

%p 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 A065858 := proc(n) A002808(ithprime(n)) ; end proc:

%p A145351 := proc(n) c := A065858(n) ; if isprime(A020639(c) + A006530(c)) then printf("%d,",c) ; end if; end proc:

%p seq(A145351(n),n=1..400) ; # _R. J. Mathar_, May 01 2010

%t 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 Cf. A000040, A002808, A020639 (lpf), A006530 (gpf).

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 04 2009

%E Corrected (inserted 20 from n=5, 30 from n=8, removed 200) and extended beyond 204 by _R. J. Mathar_, May 01 2010

%E Edited by _Jon E. Schoenfield_, Feb 07 2019

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Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)