cp's OEIS Frontend

A287147 Primes p that set a new record for the size of the smallest b > 1 such that b^(p-1) == 1 (mod p^2).

%I A287147 #17 May 19 2022 09:19:54
%S A287147 2,3,7,13,17,31,53,179,271,311,503,569,587,1231,1307,1543,1931,2647,
%T A287147 2711,3089,3917,4919,5879,6491,8933,9137,11437,13411,14431,16657,
%U A287147 21599,26053,29129,57367,58481,62071,62971,68351,70639,109721,156967,193811,216211
%N A287147 Primes p that set a new record for the size of the smallest b > 1 such that b^(p-1) == 1 (mod p^2).
%C A287147 Primes p such that A039678(i) reaches record values, where i is the index of p in A000040.
%C A287147 Records of (A185103 restricted to primes). - _Joerg Arndt_, May 29 2017
%t A287147 Function[s, Prime@ Position[s, #][[1, 1]] & /@ Union@ FoldList[Max, s]]@ Table[Function[p, b = 2; While[PowerMod[b, p - 1, p^2] != 1, b++]; b]@ Prime@ n, {n, 10^3}] (* _Michael De Vlieger_, May 21 2017 *)
%o A287147 (PARI) minb(n) = my(b=2); while(Mod(b, n^2)^(n-1)!=1, b++); b
%o A287147 my(r=0); forprime(p=1, , if(minb(p) > r, print1(p, ", "); r=minb(p)))
%o A287147 (Python)
%o A287147 from itertools import islice
%o A287147 from sympy import nextprime
%o A287147 from sympy.ntheory.residue_ntheory import nthroot_mod
%o A287147 def A287147_gen(): # generator of terms
%o A287147     c, p = 5, 3
%o A287147     yield 2
%o A287147     while True:
%o A287147         d = nthroot_mod(1,p-1,p**2,True)[1]
%o A287147         if d > c:
%o A287147             c = d
%o A287147             yield p
%o A287147         p = nextprime(p)
%o A287147 A287147_list = list(islice(A287147_gen(),15)) # _Chai Wah Wu_, May 18 2022
%Y A287147 Cf. A000040, A039678, A185103, A248865, A278611.
%K A287147 nonn
%O A287147 1,1
%A A287147 _Felix Fröhlich_, May 20 2017