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

1,1

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).

Links

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

Example

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.

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;

Crossrefs

Cf. A349660, A352851.

Intersection of A352837 and A352852.

Sequence in context: A232962 A158347 A273354 * A157991 A233555 A273729

Adjacent sequences: A352123 A352124 A352125 * A352127 A352128 A352129

Keyword

nonn

Author

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

Status

approved