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%I #13 Sep 08 2022 08:46:07
%S 29,347,2203,704993,2248123,2685653,3442987,81182821,86938393,
%T 95444081,230346509,1064332433,1298596753,1829276767,2202074113,
%U 3449796071,4306879141,6740558659,8205739219,9649993009,11650768499,14225261327,15124198183,19968681493,21415471837
%N Primes of the form prime(k)^3 + k.
%H K. D. Bajpai, <a href="/A239743/b239743.txt">Table of n, a(n) for n = 1..7000</a>
%e 29 is in the sequence because prime(2)^3 + 2 = 29, which is prime.
%e 347 is in the sequence because prime(4)^3 + 4 = 347, which is prime.
%p KD := proc() local a,b; a:= ithprime(n); b:=a^3+n; if isprime(b) then RETURN (b); fi; end: seq(KD(), n=1..1000);
%t Select[Table[Prime[k]^3 + k, {k, 1000}], PrimeQ]
%o (PARI) s=[]; for(k=1, 1000, n=prime(k)^3+k; if(isprime(n), s=concat(s, n))); s \\ _Colin Barker_, Mar 26 2014
%o (Magma) [q: k in [1..1000] | IsPrime(q) where q is NthPrime(k)^3+k]; // _Bruno Berselli_, Mar 26 2014
%Y Cf. A000040 (prime numbers).
%Y Cf. A184935 (primes: k^2 + prime(k)).
%Y Cf. A188831 (primes: k^2 - prime(k)).
%Y Cf. A229203 (primes: k^3 - prime(k)).
%Y Cf. A061068 (primes: prime(k) + k)
%Y Cf. A212304 (primes: prime(k)^2 + k).
%K nonn
%O 1,1
%A _K. D. Bajpai_, Mar 26 2014
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