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A341934 Primes p such that 2*p*q-2*q*r+r*s is prime, where p,q,r,s are consecutive primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Feb 23 2021
STATUS
approved

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Last modified February 21 05:17 EST 2024. Contains 370219 sequences. (Running on oeis4.)