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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 A358798 A102348 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 February 21 05:17 EST 2024. Contains 370219 sequences. (Running on oeis4.)