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A342505 Primes p such that (q*s-p*r)/2 is prime, where p,q,r,s are consecutive primes. 5


%S 3,67,313,359,443,719,773,971,991,1063,1163,1229,1361,1433,1451,1459,

%T 1697,1733,1877,2087,2273,2377,2417,2473,2531,2659,2879,2953,3041,

%U 3203,3559,3673,3719,4003,4091,4691,4861,5107,5179,5261,5783,6217,6317,6373,6833,6907,6971,7187,7297,7309,7349

%N Primes p such that (q*s-p*r)/2 is prime, where p,q,r,s are consecutive primes.

%H Robert Israel, <a href="/A342505/b342505.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 313 is a term because 313, 317, 331, 337 are consecutive primes and (317*337-313*331)/2 = 1613 is prime.

%p R:= NULL: count:= 0:

%p q:= 3: r:= 5: s:= 7:

%p while count < 100 do

%p p:= q; q:= r; r:= s; s:= nextprime(s);

%p if isprime((q*s-p*r)/2) then

%p count:= count+1; R:= R, p;

%p fi

%p od:

%p R;

%Y Cf. A342504, A342508, A342509.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Mar 14 2021

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Last modified December 1 20:41 EST 2021. Contains 349435 sequences. (Running on oeis4.)