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A321891
Prime numbers of the form p^3 + q, where p and q are primes.
1
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
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
Sequence in context: A109650 A284037 A338570 * A153421 A050265 A176871
KEYWORD
nonn
AUTHOR
Pierandrea Formusa, Nov 20 2018
EXTENSIONS
More terms from Amiram Eldar, Nov 21 2018
STATUS
approved