A341934 Primes p such that 2*p*q-2*q*r+r*s is prime, where p,q,r,s are consecutive primes.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 73, 101, 107, 109, 137, 191, 199, 251, 257, 293, 317, 349, 353, 421, 461, 571, 647, 659, 683, 773, 787, 811, 827, 853, 859, 877, 883, 887, 919, 929, 941, 997, 1031, 1087, 1319, 1429, 1453, 1471, 1481, 1483, 1543, 1567, 1627, 1697, 1699, 1721, 1723, 1753, 1789

Offset

1,1

Comments

Includes the first 10 primes.

If p is prime, the next four primes are p+2, p+6, p+12 and p+14, and p^2+6*p+48 is prime, then the twin primes p and p+2 are in the sequence, with the same value of A341937.

Links

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

Example

a(5) = 11 is a term because (p,q,r,s)=(11,13,17,19) are consecutive primes with 2*p*q-2*q*r+r*s = 167, which is prime.

Maple

P:= select(isprime, [2, seq(i, i=3..10000, 2)]):
B:= select(i -> isprime(P[i+2]*P[i+3]-2*P[i+1]*(P[i+2]-P[i])), [$1..nops(P)-3]):
P[B];

Prog

(Python)
from sympy import isprime, nextprime
p, q, r, s, A341934_list=2, 3, 5, 7, []
while p < 10**6:
    if isprime(2*q*(p-r)+r*s):
        A341934_list.append(p)
    p, q, r, s = q, r, s, nextprime(s) # Chai Wah Wu, Feb 24 2021

Crossrefs

Cf. A341937.

Sequence in context: A028864 A342063 A067903 * A224229 A358798 A102348

Adjacent sequences: A341931 A341932 A341933 * A341935 A341936 A341937

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 23 2021

Status

approved