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

%I A130135 #24 Mar 24 2023 11:18:26
%S A130135 2,4,12,30,40,42,62,66,70,72,84,88,98,112,130,150,180,248,264,298,336,
%T A130135 342,354,408,438,450,468,482,486,546,550,558,602,606,682,686,700,710,
%U A130135 720,732,744,770,774,804,840,848,854,948,968,976,994,996,1048,1056
%N A130135 Numbers k such that prime(k^3) - k is prime.
%H A130135 Charles R Greathouse IV, <a href="/A130135/b130135.txt">Table of n, a(n) for n = 1..5000</a>
%e A130135 a(1)=2 because prime(2^3) - 2 = 19 - 2 = 17 (a prime),
%e A130135 a(2)=4 because prime(4^3) - 4 = 311 - 4 = 307 (a prime),
%e A130135 a(3)=12 because prime(12^3) - 12 = 14741 (a prime), ...
%p A130135 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);
%t A130135 Select[Range[1100],PrimeQ[Prime[#^3]-#]&] (* _Harvey P. Dale_, Mar 24 2023 *)
%o A130135 (PARI) is(k) = isprime(prime(k^3)-k); \\ _Jinyuan Wang_, Apr 10 2020
%Y A130135 Cf. A064269 (prime(k) - k is prime), A105962 (prime(k^2) - k is prime).
%K A130135 nonn,less
%O A130135 1,1
%A A130135 _Jani Melik_, Aug 01 2007
%E A130135 a(18)-a(32) from _Jinyuan Wang_, Apr 10 2020
%E A130135 a(33)-a(44) from _Tyler NeSmith_, Apr 15 2022
%E A130135 a(45)-a(54) from _Jon E. Schoenfield_, Apr 15 2022