cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A262264 Primes that are less than the square of their least positive primitive root.

This page as a plain text file.
%I A262264 #26 Sep 15 2022 02:15:08
%S A262264 3,7,23,191,409
%N A262264 Primes that are less than the square of their least positive primitive root.
%C A262264 Alternatively, primes such that the least positive primitive root is greater than the square root of p.
%C A262264 Next term is greater than 10^9.
%D A262264 References and links at A001918.
%e A262264 The least primitive root of 23 is 5; 5^2 is greater than 23, so 23 is in the sequence.
%e A262264 The least primitive root of 409 is 21; 21^2 = 441 is greater than 409, so 409 is in the sequence.
%e A262264 41 is not in the sequence because its least primitive root is 6, and 6^2 < 41.
%t A262264 Select[Prime[Range[1000]], PrimitiveRoot[#]^2 > # &]
%o A262264 (PARI) /* the following assumes that znprimroot() returns the smallest primitive root */
%o A262264 forprime(p=2,10^9,my(g=znprimroot(p));if(lift(g)^2>p,print1(p,", "))); \\ _Joerg Arndt_, Sep 17 2015
%o A262264 (Python)
%o A262264 from itertools import islice, count
%o A262264 from sympy import prime, primitive_root
%o A262264 def A262264_gen(): # generator of terms
%o A262264     return filter(lambda p: p < primitive_root(p)**2,(prime(n) for n in count(1)))
%o A262264 A262264_list = list(islice(A262264_gen(),5)) # _Chai Wah Wu_, Sep 14 2022
%Y A262264 Cf. A001918 (least positive primitive root of n-th prime).
%K A262264 nonn,more
%O A262264 1,1
%A A262264 _Dale Taylor_, Sep 17 2015