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

29, 347, 2203, 704993, 2248123, 2685653, 3442987, 81182821, 86938393, 95444081, 230346509, 1064332433, 1298596753, 1829276767, 2202074113, 3449796071, 4306879141, 6740558659, 8205739219, 9649993009, 11650768499, 14225261327, 15124198183, 19968681493, 21415471837

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..7000

Example

29 is in the sequence because prime(2)^3 + 2 = 29, which is prime.
347 is in the sequence because prime(4)^3 + 4 = 347, which is prime.

Maple

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);

Mathematica

Select[Table[Prime[k]^3 + k, {k, 1000}], PrimeQ]

Prog

(PARI) s=[]; for(k=1, 1000, n=prime(k)^3+k; if(isprime(n), s=concat(s, n))); s \\ Colin Barker, Mar 26 2014
(Magma) [q: k in [1..1000] | IsPrime(q) where q is NthPrime(k)^3+k]; // Bruno Berselli, Mar 26 2014

Crossrefs

Cf. A000040 (prime numbers).

Cf. A184935 (primes: k^2 + prime(k)).

Cf. A188831 (primes: k^2 - prime(k)).

Cf. A229203 (primes: k^3 - prime(k)).

Cf. A061068 (primes: prime(k) + k)

Cf. A212304 (primes: prime(k)^2 + k).

Sequence in context: A160442 A125417 A156640 * A022689 A234810 A077516

Adjacent sequences: A239740 A239741 A239742 * A239744 A239745 A239746

Keyword

nonn

Author

K. D. Bajpai, Mar 26 2014

Status

approved