A330478 - OEIS

%I #11 Dec 17 2019 07:47:00

%S 33,1718,4174,7971,8434,11114,13011,14005,16645,17571,29787,30574,

%T 43647,58414,63177,65006,69694,71794,87218,95314,97827,104485,125738,

%U 126394,150334,193594,196341,198694,200378,201094,212631,212847,227554,239314,243591,254427,276085,277594,288818,291514

%N Semiprimes A001358(k) = p*q such that p*q+p+q and r*s+r+s are consecutive primes, where A001358(k+1)=r*s.

%H Robert Israel, <a href="/A330478/b330478.txt">Table of n, a(n) for n = 1..1000</a>

%e a(3)=4174=2*2087, the next semiprime is 4178=2*2089, and 4174+2+2087=6263 and 4178+2+2089=6269 are consecutive primes.

%p g:= proc(n) local F;

%p   F:= ifactors(n)[2];

%p   if nops(F)=2 then n+F[1][1]+F[2][1] else n+2*F[1][1] fi

%p end proc:

%p SP:= select(t -> numtheory:-bigomega(t)=2, [seq(i,i=4..3*10^5)]):

%p nSP:= nops(SP):

%p P1:= map(g, SP):

%p SP[select(t -> isprime(P1[t]) and nextprime(P1[t])=P1[t+1], [$1..nSP-1])];

%t Select[Partition[Union@ Apply[Join, Table[Flatten@ {p #, Sort[{p, #}]} & /@ Prime@ Range@ PrimePi@ Floor[Max[#]/p], {p, #}]] &@ Prime@ Range[3*10^4], 2, 1], And[AllTrue[{#1, #2}, PrimeQ], #2 == NextPrime@ #1] & @@ {Total@ #1, Total@ #2} & @@ # &][[All, 1, 1]] (* _Michael De Vlieger_, Dec 15 2019 *)

%Y Cf. A001358.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 15 2019