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A352852 Primes p such that, if q is the next prime, p^2 + q is a prime times a power of 10.

%I A352852 #14 Apr 09 2022 02:24:18
%S A352852 2,523,701,2213,2243,3041,3701,4177,4423,6451,7673,8447,8513,9587,
%T A352852 11131,15233,15331,15583,17519,19051,20071,20333,22483,24767,25951,
%U A352852 26633,28183,28771,28901,30773,33461,33713,38803,39419,39989,41627,42131,43237,44633,50321,50333,51991,53551,54713,56687
%N A352852 Primes p such that, if q is the next prime, p^2 + q is a prime times a power of 10.
%C A352852 Primes prime(k) such that when any trailing zeros are removed from A352851(k), the result is prime.
%H A352852 Robert Israel, <a href="/A352852/b352852.txt">Table of n, a(n) for n = 1..10000</a>
%e A352852 a(3) = 701 is a term because it is prime, 709 is the next prime, and 701^2 + 709 = 492110 where 49211 is prime.
%p A352852 R:= NULL: count:= 0:
%p A352852 q:= 2:
%p A352852 while count < 100 do
%p A352852   p:= q; q:= nextprime(p);
%p A352852   v:= p^2+q;
%p A352852   if v mod 10 = 0 then v:= v/10^min(padic:-ordp(v, 2), padic:-ordp(v, 5)) fi;
%p A352852   if isprime(v) then count:= count+1; R:= R, p; fi;
%p A352852 od:
%p A352852 R;
%t A352852 f[n_] := n/10^IntegerExponent[n, 10]; Select[Range[60000], PrimeQ[#] && PrimeQ[f[#^2 + NextPrime[#]]] &] (* _Amiram Eldar_, Apr 07 2022 *)
%Y A352852 Cf. A352837, A352851.
%K A352852 nonn
%O A352852 1,1
%A A352852 _J. M. Bergot_ and _Robert Israel_, Apr 05 2022