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

Author

K. D. Bajpai, May 12 2015

Keywords

• nonn

Comments

All terms are even.

Examples

			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.
		

Links

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

Crossrefs

Cf. A141526, A212881.

Programs

Magma

[n: n in [1..20000] | IsPrime(n^3+NthPrime(n)) and IsPrime(n^3-NthPrime(n))];

Mathematica

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

PARI

for(n=1, 1e5, if(isprime(n^3 + prime(n)) && isprime(n^3 - prime(n)), print1(n,", ")))

Formula

Intersection of A141526 and A212881.