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A225726 Lesser of two consecutive primes, p < q, such that p*q + p - q and p*q - p + q are also consecutive primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Paolo P. Lava and 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.

MAPLE

with(numtheory); listA225726:=proc(q) local a, b, n;

for n from 1 to q do a:=ithprime(n); b:=nextprime(a);

if isprime(a*b+a-b) and a*b-a+b=nextprime(a*b+a-b) then print(a);

fi; od; end: listA225726(10^6); # Paolo P. Lava, May 14 2013

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 A238265 A203015

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

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Last modified November 30 17:12 EST 2021. Contains 349424 sequences. (Running on oeis4.)