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A342506 Primes p such that (p*s+q*r)/2 is prime, where p,q,r,s are consecutive primes. 4


%S 5,7,13,97,107,157,223,311,353,419,479,541,673,691,701,839,877,1049,

%T 1193,1297,1423,1559,1747,1787,2017,2239,2341,2383,2459,2633,2719,

%U 2797,2833,2851,3121,3209,3359,3391,3581,3613,3617,3671,4219,4261,4729,4831,4933,4993,5023,5309,5393,5657,5867

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

%H Robert Israel, <a href="/A342506/b342506.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 13 is a term because 13, 17, 19, 23 are consecutive primes with (13*23+17*19)/2 = 311 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((p*s+q*r)/2) then

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

%p fi

%p od:

%p R;

%Y Cf. A342504, A342508.

%K nonn

%O 1,1

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

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Last modified November 29 10:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)