A268475 Numbers n such that n^3 +/- 2 and 3*n +/- 2 are all prime.

435, 555, 2415, 31635, 38025, 44835, 80625, 88335, 97455, 98505, 99435, 124335, 142065, 145095, 165375, 176055, 204765, 246435, 279225, 293475, 310095, 315555, 332085, 344745, 348735, 376935, 392415, 443595, 462105, 467385, 482355, 581415, 609555, 626775, 636015

Offset

1,1

Comments

All the terms in this sequence are congruent to 0 (mod 5).

Each term in this sequence yields two sets of cousin prime pairs i.e., for n = 435 -> {82312877, 82312873} and {1307, 1303}.

All terms are congruent to 15 mod 30. - Robert Israel, Feb 05 2016

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

435 is in the sequence because 435^3 + - 2 =  82312877, 82312873; 3*435 + - 2 = 1307, 1303 are all prime.
555 is in the sequence because 555^3 + - 2 =  170953877, 170953873; 3*555 + - 2 = 1667, 1663 are all prime.

Maple

select(n -> andmap(isprime, [n^3 + 2, n^3 - 2, 3*n + 2, 3*n - 2]), [seq(p, p=1.. 10^6)]);

Mathematica

Select[Range[1000000], PrimeQ[#^3 + 2] && PrimeQ[#^3 - 2] && PrimeQ[3 # + 2] && PrimeQ[3 # - 2] &]

Prog

(PARI) for(n = 1, 1e5, if( isprime(n^3 + 2) && isprime(n^3 - 2) && isprime(3*n + 2) && isprime(3*n - 2), print1(n ", ")))
(Magma) [n : n in [1..1e5] | IsPrime(n^3 + 2) and IsPrime(n^3 - 2) and IsPrime(3*n + 2) and IsPrime(3*n - 2)];

Crossrefs

Cf. A024893, A090121, A108701, A153183, A157834.

Sequence in context: A054987 A054905 A160353 * A212227 A369153 A237302

Adjacent sequences: A268472 A268473 A268474 * A268476 A268477 A268478

Keyword

nonn

Author

K. D. Bajpai, Feb 05 2016

Status

approved