A321891 Prime numbers of the form p^3 + q, where p and q are primes.

11, 13, 19, 29, 31, 37, 61, 67, 79, 97, 109, 127, 139, 157, 181, 199, 241, 271, 277, 367, 397, 409, 439, 457, 487, 499, 571, 577, 601, 607, 661, 691, 709, 727, 751, 769, 829, 919, 937, 991, 1021, 1039, 1069, 1117, 1171, 1201, 1231, 1237, 1291, 1297, 1327, 1381

Offset

1,1

Comments

Union of A048636 and A092402. - Michel Marcus, Nov 21 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

37 is prime and 37 = 2^3 + 29, where 2 and 29 are primes, therefore 37 is a term.

Maple

N:= 2000: # to get terms <= N
A1:= select(t -> isprime(t) and isprime(t-8), {11, seq(i, i=13 ..N, 6)}):
v:= floor((N-2)^(1/3)):
B:= select(t -> isprime(t) and isprime(t^3+2), {3, seq(i, i=5..v, 6)}):
sort(convert(A1 union map(t -> t^3+2, B), list)); # Robert Israel, Mar 05 2020

Mathematica

nmax=4; Select[Union[Prime[Range[nmax]]^3 + 2, Prime[Range[Prime[nmax]^3]] + 8], PrimeQ] (* Amiram Eldar, Nov 21 2018 *)

Prog

(MiniZinc)
include "globals.mzn";
int: n = 2;
int: max_val = 1200000;
array[1..n+1] of var 2..max_val: x;
% primes between 2..max_valset of int:
prime = 2..max_val diff { i | i in 2..max_val, j in 2..ceil(sqrt(i)) where i mod j = 0} ;
set of int: primes; primes = prime union {2};
solve satisfy;
constraint all_different(x) /\ x[1] in primes /\ x[2] in primes /\ x[3] in primes /\
pow(x[1], 3)+pow(x[2], 1)= x[3] ;
output [ show(x)]

Crossrefs

Cf. A048636, A092402.

Sequence in context: A109650 A284037 A338570 * A153421 A050265 A176871

Adjacent sequences: A321888 A321889 A321890 * A321892 A321893 A321894

Keyword

nonn

Author

Pierandrea Formusa, Nov 20 2018

Extensions

More terms from Amiram Eldar, Nov 21 2018

Status

approved