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A352837 Primes p such that, if q is the next prime, p + q^2 is a prime times a power of 10.

%I A352837 #15 Apr 09 2022 02:24:26
%S A352837 2,409,709,1249,3229,4621,6709,7069,7129,7489,8209,9241,9661,10789,
%T A352837 11149,13381,13789,15349,17509,20641,21169,21961,23509,25819,26449,
%U A352837 28309,28729,32029,32089,34849,35089,35809,37321,37369,39769,40129,42169,42349,42709,42901,42979,44179,46489,47269,47809
%N A352837 Primes p such that, if q is the next prime, p + q^2 is a prime times a power of 10.
%C A352837 Primes prime(k) such that when any trailing zeros are removed from A349660(k), the result is prime.
%H A352837 Robert Israel, <a href="/A352837/b352837.txt">Table of n, a(n) for n = 1..10000</a>
%e A352837 a(3) = 709 is a term because 709 and 719 are consecutive primes, 709 + 719^2 = 517670, and 51767 is prime.
%p A352837 R:= NULL: count:= 0:
%p A352837 q:= 2:
%p A352837 while count < 100 do
%p A352837   p:= q; q:= nextprime(p);
%p A352837   v:= p+q^2;
%p A352837   if v mod 10 = 0 then v:= v/10^min(padic:-ordp(v,2),padic:-ordp(v,5)) fi;
%p A352837   if isprime(v) then count:= count+1; R:= R,p; fi;
%p A352837 od:
%p A352837 R;
%t A352837 f[n_] := n/10^IntegerExponent[n, 10]; Select[Range[50000], PrimeQ[#] && PrimeQ[f[# + NextPrime[#]^2]] &] (* _Amiram Eldar_, Apr 07 2022 *)
%Y A352837 Cf. A349660, A352848.
%K A352837 nonn
%O A352837 1,1
%A A352837 _J. M. Bergot_ and _Robert Israel_, Apr 05 2022