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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

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 A102348 A161929

Adjacent sequences:  A341931 A341932 A341933 * A341935 A341936 A341937

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 27 07:47 EDT 2021. Contains 348272 sequences. (Running on oeis4.)