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A352126 Primes p such that, if q is the next prime, both p+q^2 and p^2+q are primes times powers of 10.

%I A352126 #37 Apr 07 2022 10:51:04
%S A352126 2,4806589,8369989,11168569,20666869,25068349,25465249,29046469,
%T A352126 37597849,40593349,44242669,45405889,47975869,49637149,50057569,
%U A352126 51468349,57060469,59570449,64602589,64707889,65940769,70752049,75879169,81799789,87845869,90277249,92415649,93315889,95458249,97225069
%N A352126 Primes p such that, if q is the next prime, both p+q^2 and p^2+q are primes times powers of 10.
%C A352126 Primes prime(k) such that when any trailing zeros are removed from A349660(k) and A352851(k), the results are prime.
%C A352126 Except for 2, each term and the next prime == 19 (mod 30).
%H A352126 Robert Israel, <a href="/A352126/b352126.txt">Table of n, a(n) for n = 1..250</a>
%e A352126 a(3) = 8369989 is a term because it is prime, the next prime is 8370049,
%e A352126 8369989+8370049^2 = 70057728632390, 8369989^2+8370049 = 70056724230170, and 7005772863239 and 7005672423017 are prime.
%p A352126 R:= NULL: count:= 0:
%p A352126 q:= 2:
%p A352126 while count < 30 do
%p A352126   p:= q; q:= nextprime(p);
%p A352126   w:= p+q^2;
%p A352126   m:= padic:-ordp(w,2);
%p A352126   if padic:-ordp(w,5) <> m then next fi;
%p A352126   if m > 0 then w:= w/10^m fi;
%p A352126   if not isprime(w) then next fi;
%p A352126   v:= p^2+q;
%p A352126   m:= padic:-ordp(v,2);
%p A352126   if padic:-ordp(v,5) <> m then next fi;
%p A352126   if m > 0 then v:= v/10^m fi;
%p A352126   if isprime(v) then count:= count+1; R:= R, p; fi
%p A352126 od:
%p A352126 R;
%Y A352126 Cf. A349660, A352851.
%Y A352126 Intersection of A352837 and A352852.
%K A352126 nonn
%O A352126 1,1
%A A352126 _J. M. Bergot_ and _Robert Israel_, Apr 05 2022