A257788 Numbers n such that n^3+prime(n) and n^3-prime(n) are prime.

2, 66, 228, 696, 1416, 2172, 3000, 3384, 3732, 4314, 4524, 4554, 5070, 5220, 5412, 5826, 5844, 6636, 7422, 7662, 7932, 8148, 8832, 9528, 10092, 10242, 10746, 11670, 11682, 11820, 12918, 13266, 14430, 14580, 15216, 15300, 15534, 15864, 16542, 16782, 16932, 17670

Offset

1,1

Comments

All terms are even.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..6436

Formula

Intersection of A141526 and A212881.

Example

2 is in the sequence: 2^3 + prime(2) = 11; 2^3 - prime(2) = 5; both are prime.
66 is in the sequence: 66^3 + prime(66) = 287813; 66^3 - prime(66) = 287179; both are prime.

Mathematica

Select[Range[30000], PrimeQ[#^3 + Prime[#]] && PrimeQ[#^3 - Prime[#]] &]
Select[Range[18000], AllTrue[#^3+{Prime[#], -Prime[#]}, PrimeQ]&] (* Harvey P. Dale, Aug 10 2023 *)

Prog

(PARI) for(n=1, 1e5, if(isprime(n^3 + prime(n)) && isprime(n^3 - prime(n)), print1(n, ", ")))
(Magma)  [n: n in [1..20000] | IsPrime(n^3+NthPrime(n)) and IsPrime(n^3-NthPrime(n))];

Crossrefs

Cf. A141526, A212881.

Sequence in context: A098089 A304934 A075809 * A349108 A226409 A226338

Adjacent sequences: A257785 A257786 A257787 * A257789 A257790 A257791

Keyword

nonn

Author

K. D. Bajpai, May 12 2015

Status

approved