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

2, 523, 701, 2213, 2243, 3041, 3701, 4177, 4423, 6451, 7673, 8447, 8513, 9587, 11131, 15233, 15331, 15583, 17519, 19051, 20071, 20333, 22483, 24767, 25951, 26633, 28183, 28771, 28901, 30773, 33461, 33713, 38803, 39419, 39989, 41627, 42131, 43237, 44633, 50321, 50333, 51991, 53551, 54713, 56687

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 05 2022

Keywords

• nonn

Comments

Primes prime(k) such that when any trailing zeros are removed from A352851(k), the result is prime.

Examples

			a(3) = 701 is a term because it is prime, 709 is the next prime, and 701^2 + 709 = 492110 where 49211 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A352837, A352851.

Programs

Maple

R:= NULL: count:= 0:
q:= 2:
while count < 100 do
  p:= q; q:= nextprime(p);
  v:= p^2+q;
  if v mod 10 = 0 then v:= v/10^min(padic:-ordp(v, 2), padic:-ordp(v, 5)) fi;
  if isprime(v) then count:= count+1; R:= R, p; fi;
od:
R;

Mathematica

f[n_] := n/10^IntegerExponent[n, 10]; Select[Range[60000], PrimeQ[#] && PrimeQ[f[#^2 + NextPrime[#]]] &] (* Amiram Eldar, Apr 07 2022 *)