A225726 Lesser of two consecutive primes, p < q, such that p*q + p - q and p*q - p + q are also consecutive primes.

2, 3, 23, 991, 1621, 3301, 5471, 5683, 6563, 6581, 7829, 10061, 13841, 16981, 18199, 26203, 28403, 32003, 35671, 37561, 41771, 42571, 55529, 55603, 58543, 60251, 71861, 75931, 92809, 98993, 103669, 104281, 116953, 117751, 125591, 139969, 142151, 155509, 160073

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 100 terms from Lava)

Example

2 prime, 3 next-prime and 2*3 + 2 - 3 = 5 prime, 2*3 - 2 + 3 = 7 next-prime, so a(1) = 2.

Mathematica

acpQ[{p_, q_}]:=Module[{c=p*q+p-q}, PrimeQ[c]&&NextPrime[c]==p*q-p+q]; Select[ Partition[Prime[Range[15000]], 2, 1], acpQ][[All, 1]] (* Harvey P. Dale, Oct 09 2017 *)

Prog

(PARI) p=2; forprime(q=3, 1e6, my(pq=p*q); if(isprime(pq+p-q) && nextprime(pq+p-q+1)==pq-p+q, print1(p", ")); p=q) \\ Charles R Greathouse IV, Mar 18 2014

Crossrefs

Cf. A154553.

Sequence in context: A154553 A160341 A092388 * A076530 A360225 A238265

Adjacent sequences: A225723 A225724 A225725 * A225727 A225728 A225729

Keyword

nonn

Author

Irina Gerasimova, May 13 2013

Extensions

Added a(5), a(6) and a(20)-a(39) by Paolo P. Lava, May 14 2013

Status

approved