A330478 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.

33, 1718, 4174, 7971, 8434, 11114, 13011, 14005, 16645, 17571, 29787, 30574, 43647, 58414, 63177, 65006, 69694, 71794, 87218, 95314, 97827, 104485, 125738, 126394, 150334, 193594, 196341, 198694, 200378, 201094, 212631, 212847, 227554, 239314, 243591, 254427, 276085, 277594, 288818, 291514

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 15 2019

Keywords

• nonn

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358.

Programs

Maple

g:= proc(n) local F;
  F:= ifactors(n)[2];
  if nops(F)=2 then n+F[1][1]+F[2][1] else n+2*F[1][1] fi
end proc:
SP:= select(t -> numtheory:-bigomega(t)=2, [seq(i,i=4..3*10^5)]):
nSP:= nops(SP):
P1:= map(g, SP):
SP[select(t -> isprime(P1[t]) and nextprime(P1[t])=P1[t+1], [$1..nSP-1])];

Mathematica

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 *)