cp's OEIS Frontend

A239743 Primes of the form prime(k)^3 + k.

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