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.

2, 4806589, 8369989, 11168569, 20666869, 25068349, 25465249, 29046469, 37597849, 40593349, 44242669, 45405889, 47975869, 49637149, 50057569, 51468349, 57060469, 59570449, 64602589, 64707889, 65940769, 70752049, 75879169, 81799789, 87845869, 90277249, 92415649, 93315889, 95458249, 97225069

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) and A352851(k), the results are prime.

Except for 2, each term and the next prime == 19 (mod 30).

Examples

			a(3) = 8369989 is a term because it is prime, the next prime is 8370049,
8369989+8370049^2 = 70057728632390, 8369989^2+8370049 = 70056724230170, and 7005772863239 and 7005672423017 are prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A349660, A352851.

Intersection of A352837 and A352852.

Programs

Maple

R:= NULL: count:= 0:
q:= 2:
while count < 30 do
  p:= q; q:= nextprime(p);
  w:= p+q^2;
  m:= padic:-ordp(w,2);
  if padic:-ordp(w,5) <> m then next fi;
  if m > 0 then w:= w/10^m fi;
  if not isprime(w) then next fi;
  v:= p^2+q;
  m:= padic:-ordp(v,2);
  if padic:-ordp(v,5) <> m then next fi;
  if m > 0 then v:= v/10^m fi;
  if isprime(v) then count:= count+1; R:= R, p; fi
od:
R;