cp's OEIS Frontend

A350179 Primes of the form ( A349309(n) + 1 ) ^ (1/3).

%I A350179 #63 Jul 18 2022 09:48:27
%S A350179 2,3,5,7,11,13,23,29,31,43,47,53,59,61,67,71,79,83,101,103,107,131,
%T A350179 139,149,151,157,167,173,179,191,197,211,223,227,229,239,263,269,277,
%U A350179 283,293,311,317,331,347,349,359,367,373,383,389,419,421,431,439,443,461,463,467
%N A350179 Primes of the form ( A349309(n) + 1 ) ^ (1/3).
%C A350179 Equivalently, primes p such that A051903(p^3-1) < 3. - _Amiram Eldar_, Dec 26 2021
%e A350179 5 is a term since (A349309(3) + 1) ^ (1/3) = 125 ^ (1/3) = 5.
%p A350179 filter:= n -> isprime(n) and max(map(t -> t[2],ifactors(n^3-1)[2]))<3:
%p A350179 select(filter, [2,seq(i,i=3..1000,2)]); # _Robert Israel_, Dec 26 2021
%t A350179 q[p_] := PrimeQ[p] && AllTrue[FactorInteger[p^3 - 1][[;; , 2]], # < 3 &]; Select[Range[500], q] (* _Amiram Eldar_, Dec 26 2021 *)
%o A350179 (Python)
%o A350179 from itertools import count, islice
%o A350179 from sympy import prime, factorint
%o A350179 def A350179_gen(): return (p for p in (prime(n) for n in count(1)) if max(factorint(p**3-1).values()) < 3)
%o A350179 A350179_list = list(islice(A350179_gen(),30)) # _Chai Wah Wu_, Jan 24 2022
%o A350179 (PARI) isok(p) = isprime(p) && (vecmax(factor(p^3-1)[,2]) < 3); \\ _Michel Marcus_, Jul 18 2022
%Y A350179 Cf. A051903, A349309.
%K A350179 nonn
%O A350179 1,1
%A A350179 _Flávio V. Fernandes_, Dec 23 2021
%E A350179 More terms from _Michel Marcus_, Dec 25 2021