A353153 Primes p such that (q-p)*p*q+1 is prime, where q is the next prime after p.

2, 3, 5, 17, 23, 31, 41, 47, 73, 101, 107, 167, 191, 199, 227, 269, 271, 311, 331, 373, 443, 541, 569, 571, 587, 593, 619, 647, 653, 661, 733, 751, 881, 941, 977, 1031, 1063, 1103, 1117, 1123, 1187, 1307, 1427, 1433, 1451, 1499, 1553, 1637, 1709, 1747, 1753, 1811, 1889, 1949, 1973, 1987, 2069

Offset

1,1

Links

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

Example

a(3) = 5 is a term because the next prime is 7 and (7-5)*5*7+1 = 71 is prime.

Maple

R:= NULL: count := 0:
q:= 2:
while count < 100 do
  p:= q; q:= nextprime(q);
  if isprime((q-p)*p*q+1) then
    count:= count+1;
    R:= R, p;
  fi
od:
R;

Mathematica

Select[Range[2000], PrimeQ[#] && PrimeQ[((q = NextPrime[#]) - #) * # * q + 1] &] (* Amiram Eldar, Apr 27 2022 *)

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    p, q = 2, 3
    while  True:
        if isprime((q-p)*p*q+1):
            yield p
        p, q = q, nextprime(q)
print(list(islice(agen(), 20))) # Michael S. Branicky, Apr 27 2022

Crossrefs

Cf. A001223 (prime gaps).

Sequence in context: A111632 A049547 A049577 * A121558 A240679 A180474

Adjacent sequences: A353150 A353151 A353152 * A353154 A353155 A353156

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Apr 26 2022

Status

approved