A130135 Numbers k such that prime(k^3) - k is prime.

2, 4, 12, 30, 40, 42, 62, 66, 70, 72, 84, 88, 98, 112, 130, 150, 180, 248, 264, 298, 336, 342, 354, 408, 438, 450, 468, 482, 486, 546, 550, 558, 602, 606, 682, 686, 700, 710, 720, 732, 744, 770, 774, 804, 840, 848, 854, 948, 968, 976, 994, 996, 1048, 1056

Offset: 1

Author

Jani Melik, Aug 01 2007

Keywords

• nonn
• less

Examples

			a(1)=2 because prime(2^3) - 2 = 19 - 2 = 17 (a prime),
a(2)=4 because prime(4^3) - 4 = 311 - 4 = 307 (a prime),
a(3)=12 because prime(12^3) - 12 = 14741 (a prime), ...
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A064269 (prime(k) - k is prime), A105962 (prime(k^2) - k is prime).

Programs

Maple

ts_pra_3:=proc(n) local i,ans; ans := [ ]: for i from 1 to n do if (isprime(ithprime(i^(3))-i)) then ans := [ op(ans), i ]: fi: od; RETURN(ans) end: ts_pra_3(200);

Mathematica

Select[Range[1100],PrimeQ[Prime[#^3]-#]&] (* Harvey P. Dale, Mar 24 2023 *)

PARI

is(k) = isprime(prime(k^3)-k); \\ Jinyuan Wang, Apr 10 2020

Extensions

a(18)-a(32) from Jinyuan Wang, Apr 10 2020

a(33)-a(44) from Tyler NeSmith, Apr 15 2022

a(45)-a(54) from Jon E. Schoenfield, Apr 15 2022