A248480 -id:A248480 - cp's OEIS frontend

A248483 Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. The sequence gives primes Q.

13, 19, 47, 181, 317, 367, 677, 743, 811, 1031, 1489, 2347, 2381, 2477, 2749, 2777, 4729, 4951, 5189, 5657, 5851, 6287, 7297, 7583, 8287, 8867, 8969, 9001, 9049, 9463, 10103, 10733, 11261, 12713, 13109, 14009, 14747, 17393, 17749, 18679, 19081, 20399, 21157, 22541

Offset: 1

Zak Seidov, Oct 07 2014

nonn

			a(1)=13 because p=3, q=5 and P=11 and Q=13 are both prime.
a(3)=47 because p=13, q=17 and P=43 and Q=47 are both prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A181848 (primes p), A248480 (primes q), A248482 (primes P).

R:= NULL: count:= 0:
q:= 2:
while count < 100 do
  p:= q; q:= nextprime(q);
  if isprime(2*p+q) and isprime(p+2*q) then
    count:= count+1; R:= R, p+2*q
  fi
od:
R; # Robert Israel, Jan 05 2021

Select[Table[If[PrimeQ[2*Prime[j-1] + Prime[j]] && PrimeQ[Prime[j-1] + 2*Prime[j]],Prime[j-1] + 2*Prime[j],0],{j,2,2000}],#!=0&] (* Vaclav Kotesovec, Oct 08 2014 *)
2#[[2]]+#[[1]]&/@Select[Partition[Prime[Range[1000]],2,1],AllTrue[{2#[[1]]+#[[2]],2#[[2]]+ #[[1]]},PrimeQ]&]  (* Harvey P. Dale, Jan 10 2024 *)

listQ(nn) = {forprime(p=2, nn, q = nextprime(p+1); if (isprime(2*p+q) && isprime(Q=2*q+p), print1(Q, ", ")););} \\ Michel Marcus, Oct 07 2014

A248482 Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. The sequence gives primes P.

Original entry on oeis.org

11, 17, 43, 179, 313, 353, 673, 733, 809, 1021, 1481, 2333, 2371, 2473, 2741, 2767, 4721, 4931, 5179, 5647, 5849, 6277, 7283, 7573, 8273, 8863, 8941, 8999, 9041, 9437, 10093, 10723, 11239, 12703, 13099, 13999, 14737, 17383, 17729, 18671, 19079, 20389, 21143, 22531

Offset: 1

Zak Seidov, Oct 07 2014

nonn

			a(1)=11 because p=3, q=5 and P=11 and Q=13 are both prime.
a(3)=43 because p=13, q=17 and P=43 and Q=47 are both prime.

Cf. A181848(primes p), A248480(primes q), A248483(primes Q).

Select[Table[If[PrimeQ[2*Prime[j-1] + Prime[j]] && PrimeQ[Prime[j-1] + 2*Prime[j]],2*Prime[j-1] + Prime[j],0],{j,2,2000}],#!=0&] (* Vaclav Kotesovec, Oct 08 2014 *)
2#[[1]]+#[[2]]&/@Select[Partition[Prime[Range[1000]],2,1],AllTrue[ {2#[[1]]+ #[[2]],2#[[2]]+#[[1]]},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 28 2017 *)

listP(nn) = {forprime(p=2, nn, q = nextprime(p+1); if (isprime(P=2*p+q) && isprime(2*q+p), print1(P, ", ")););} \\ Michel Marcus, Oct 07 2014

cp's OEIS Frontend

A248483 Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. The sequence gives primes Q.

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