A280266 Primes such that the previous prime plus the next prime plus 1 is also prime.

5, 7, 13, 19, 31, 37, 43, 47, 53, 61, 73, 79, 89, 97, 137, 151, 167, 173, 193, 199, 223, 229, 241, 251, 271, 349, 353, 367, 379, 383, 409, 439, 457, 463, 487, 503, 521, 523, 587, 593, 619, 643, 647, 653, 727, 787, 797, 809, 829, 853, 859, 937

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

5 is in the sequence because 3 + 7 + 1 = 11, which is prime.
7 is in the sequence because 5 + 11 + 1 = 17, which is prime.
11 is not in the sequence because 7 + 13 + 1 = 21, which is not prime.

Mathematica

fQ[p_] := PrimeQ[ NextPrime[p, -1] + NextPrime[ p] +1]; Select[ Prime@ Range[2, 170], fQ] (* Robert G. Wilson v, Dec 30 2016 *)
Select[Partition[Prime[Range[200]], 3, 1], PrimeQ[#[[1]]+#[[3]]+1]&][[All, 2]] (* Harvey P. Dale, Dec 16 2018 *)

Prog

(Sage)
max_next_p = 1000
seq = []
prev_p = nth_prime(1)
p = nth_prime(2)
for next_p in primes(nth_prime(3), max_next_p):
    if is_prime(prev_p + next_p + 1):
        seq.append(p)
    prev_p = p
    p = next_p
print(seq)
(PARI) isok(n) = isprime(n) && isprime(precprime(n-1) + nextprime(n+1) + 1); \\ Michel Marcus, Dec 30 2016

Crossrefs

Cf. A005384, A005385, A006562.

Sequence in context: A227420 A099349 A167464 * A370008 A243457 A189441

Adjacent sequences: A280263 A280264 A280265 * A280267 A280268 A280269

Keyword

nonn

Author

Robert C. Lyons, Dec 30 2016

Status

approved