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A341357 Primes p such that q*r == p (mod q+r) where q and r are the next primes after p.

%I A341357 #10 Feb 10 2021 16:48:26
%S A341357 5,11,17,41,101,107,191,227,311,347,461,467,641,821,857,881,1091,1277,
%T A341357 1301,1427,1481,1487,1511,1607,1811,1871,1997,2081,2237,2267,2447,
%U A341357 2657,2687,3251,3461,3527,3671,3917,4001,4127,4517,4637,4787,4931,4967,5039,5231,5477,5501,5651,6101,6197,6827
%N A341357 Primes p such that q*r == p (mod q+r) where q and r are the next primes after p.
%C A341357 If for some k >= 0 we have q=p+2*(k+1)*(2*k+1) and r=p+2*(k+1)*(2*k+3) then p is in the sequence.  This includes A022004 in the case k=0.
%C A341357 It appears that all terms are of the above form.
%H A341357 Robert Israel, <a href="/A341357/b341357.txt">Table of n, a(n) for n = 1..10000</a>
%e A341357 a(3) = 17 is in the sequence because with p = 17, q = 19, r = 23, q*r = 437 == 17 (mod 19+23=42).
%p A341357 q:= 2: r:= 3: count:= 0: R:= NULL:
%p A341357 while count < 100 do
%p A341357   p:= q: q:= r: r:= nextprime(r);
%p A341357 if (q*r) mod (q+r) = p then count:= count+1; R:= R, p fi;
%p A341357 od:
%p A341357 R;
%Y A341357 Cf. A022004, A341322.
%K A341357 nonn
%O A341357 1,1
%A A341357 _J. M. Bergot_ and _Robert Israel_, Feb 09 2021