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.
%I A211671 #14 Apr 26 2025 04:17:20
%S A211671 2,11,47,137,691,25621,59233,2424511,2607383,78043403,1032758989,
%T A211671 80051779
%N A211671 Least prime p such that the polynomial x^n - x^(n-1) - ... - 1 (mod p) has n distinct zeros.
%C A211671 This is the characteristic polynomial of the n-step Fibonacci and Lucas sequences. For composite p, the polynomial can have more than n zeros! See A211672.
%e A211671 For p = 11, x^2-x-1 = (x+3)(x+7) (mod p).
%e A211671 For p = 47, x^3-x^2-x-1 = (x+21)(x+30)(x+42) (mod p).
%e A211671 For p = 137, x^4-x^3-x^2-x-1 = (x+12)(x+79)(x+85)(x+97) (mod p).
%t A211671 Table[poly = x^n - Sum[x^k, {k, 0, n - 1}]; k = 1; While[p = Prime[k]; cnt = 0; Do[If[Mod[poly, p] == 0, cnt++], {x, 0, p - 1}]; cnt < n, k++]; p, {n, 5}]
%o A211671 (PARI) a(n)={my(P=x^n-sum(k=0, n-1, x^k) ); forprime(p=2, oo, if(#polrootsmod(P,p)==n, return(p) ) );} \\ _Joerg Arndt_, Apr 15 2013
%Y A211671 Cf. A045468 (n=2), A106279 (n=3), A106280 (n=4), A106281 (n=5).
%Y A211671 Cf. A211672 (for composite p).
%K A211671 nonn,hard,more
%O A211671 1,1
%A A211671 _T. D. Noe_, Apr 18 2012
%E A211671 a(8)-a(10) from _Joerg Arndt_, Apr 15 2013
%E A211671 a(11)-a(12) from _Jinyuan Wang_, Apr 25 2025