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

2, 409, 709, 1249, 3229, 4621, 6709, 7069, 7129, 7489, 8209, 9241, 9661, 10789, 11149, 13381, 13789, 15349, 17509, 20641, 21169, 21961, 23509, 25819, 26449, 28309, 28729, 32029, 32089, 34849, 35089, 35809, 37321, 37369, 39769, 40129, 42169, 42349, 42709, 42901, 42979, 44179, 46489, 47269, 47809

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 A349660(k), the result is prime.

Examples

			a(3) = 709 is a term because 709 and 719 are consecutive primes, 709 + 719^2 = 517670, and 51767 is prime.
		

Links

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

Crossrefs

Cf. A349660, A352848.

Programs

Maple

R:= NULL: count:= 0:
q:= 2:
while count < 100 do
  p:= q; q:= nextprime(p);
  v:= p+q^2;
  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[50000], PrimeQ[#] && PrimeQ[f[# + NextPrime[#]^2]] &] (* Amiram Eldar, Apr 07 2022 *)