A329727 Numbers k such that k^3 +- 2 and k +- 2 are prime.

129, 1491, 1875, 2709, 5655, 6969, 10335, 14325, 14421, 17319, 26559, 35109, 37509, 43719, 50229, 52629, 101871, 102795, 104325, 105501, 120429, 127599, 132699, 136395, 137829, 157521, 172425, 173685, 179481, 186189, 191829, 211371, 219681, 221199, 229215, 234195

Offset

1,1

Comments

All terms in this sequence are divisible by 3.

Links

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Example

a(1) = 129:
  129^3 + 2 = 2146691;
  129^3 - 2 = 2146687;
  129   + 2 =     131;
  129   - 2 =     127; all four results are prime.
a(2) = 1491:
  1491^3 + 2 = 3314613773;
  1491^3 - 2 = 3314613769;
  1491   + 2 =       1493;
  1491   - 2 =       1489; all four results are prime.

Mathematica

Select[Range[500000], PrimeQ[#^3 + 2] && PrimeQ[#^3 - 2] && PrimeQ[# + 2] && PrimeQ[# - 2] &]

Prog

(Magma) [k:k in [1..250000]|forall{m:m in [-2, 2]|IsPrime(k+m) and IsPrime(k^3+m)}]; // Marius A. Burtea, Nov 20 2019
(PARI) isok(k) = isprime(k-2) && isprime(k+2) && isprime(k^3-2) && isprime(k^3+2); \\ Michel Marcus, Nov 24 2019
(PARI) list(lim)=my(v=List(), p=127, k); forprime(q=131, lim+2, if(q-p==4 && isprime((k=p+2)^3-2) && isprime(k^3+2), listput(v, k)); p=q); Vec(v) \\ Charles R Greathouse IV, May 06 2020

Crossrefs

Intersection of A038599, A067200, and A087679.

Cf. A040976, A052147, A090121, A268043, A268186.

Sequence in context: A046286 A341552 A251095 * A209532 A233305 A268266

Adjacent sequences: A329724 A329725 A329726 * A329728 A329729 A329730

Keyword

nonn

Author

K. D. Bajpai, Nov 19 2019

Status

approved