OFFSET
1,1
COMMENTS
Conjecture: the only primes not in the sequence are
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 73, 79, 97, 101, 103, 109, 127, 139, 199, 229, 463. - Robert Israel, Aug 17 2018
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
59 belongs to this sequence as 59 = 3^3 + 5^2 + 7, with 3, 5 and 7 all different primes.
MAPLE
N:= 500: # to get all terms <= N
p1:= 2: Res:= {}:
do
p1:= nextprime(p1);
if p1^3 + 3^2+5 > N then break fi;
p2:= 2;
do
p2:= nextprime(p2);
if p2 = p1 then next fi;
if p1^3 + p2^2 + 3 > N then break fi;
p3:= 2;
do
p3:= nextprime(p3);
if p3=p1 or p3=p2 then next fi;
v:= p1^3 + p2^2 + p3;
if v > N then break fi;
if isprime(v) then Res:= Res union {v} fi
od od od:
sort(convert(Res, list)); # Robert Israel, Aug 17 2018
MATHEMATICA
v[t_] := Prime@Range@PrimePi@t; up=500; Union@ Reap[Do[If[ PrimeQ[p = p1^3 + p2^2 + p3] && p1!=p2 && p2!=p3 && p3!=p1, Sow@p], {p1, v[up^(1/3)]}, {p2, v@Sqrt[up - p1^3]}, {p3, v[up - p1^3 - p2^2]}]][[2, 1]] (* Giovanni Resta, Jul 18 2018 *)
PROG
(MiniZinc)
%Model to get all primes less than 300 of this sequence
include "globals.mzn";
int: n = 3;
int: max_val = 300;
array[1..n+1] of var 2..max_val: x;
% primes between 2..max_val
set 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 /\ x[4] in primes /\ pow(x[1], 3)+pow(x[2], 2)+pow(x[3], 1) = x[4];
output [ show(x[4]) ];
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Pierandrea Formusa, Jul 17 2018
STATUS
approved