A280326 Primes such that the previous prime plus the next prime minus 1 is also prime.

11, 17, 23, 29, 37, 41, 59, 67, 71, 73, 83, 89, 101, 107, 131, 137, 157, 179, 191, 211, 233, 311, 317, 331, 337, 359, 419, 431, 443, 461, 467, 479, 521, 523, 541, 547, 557, 599, 607, 613, 617, 631, 683, 701, 727, 743, 751, 757, 809, 881, 887, 953, 991, 997, 1013, 1031, 1033, 1039, 1049, 1061, 1063

Offset

1,1

Comments

Intersection with A280266: 37, 73, 89, 137, 521, 523, 727, 809, 1013, ..., .

Primes that are missing from the union with A280266: 2, 3, 103, 109, ..., .

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..4700

Example

17 is in the sequence since 13 + 19 - 1 = 31 which is the eleventh prime.

Mathematica

fQ[p_] := PrimeQ[ NextPrime[p, -1] + NextPrime[ p] -1]; Select[ Prime@ Range[2, 170], fQ]

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)

Crossrefs

Cf. A280266.

Sequence in context: A175888 A209624 A243153 * A160129 A275682 A265402

Adjacent sequences: A280323 A280324 A280325 * A280327 A280328 A280329

Keyword

nonn,easy

Author

Robert C. Lyons and Robert G. Wilson v, Dec 31 2016

Status

approved