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 A141305 #17 Jan 05 2025 19:51:38 %S A141305 7,11,23,59,107,167,263,347,359,587,839,887,983,1019,1307,1319,2039, %T A141305 2459,2903,2999,3467,3803,3863,3947,4139,4283,4679,4919,5099,5387, %U A141305 5399,5483,5639,5879,5927,6599,6827,6983,7079,7559,7607,7703,8039,8699,8747 %N A141305 Primes p such that q=(p-1)/2 is also prime and 2 is a primitive root mod q; that is, q is in A001122. %C A141305 These primes are a subset of the safe primes, A005385. These primes produce the longest possible cycles, (p-3)/2, in the squaring mod p map. See A037178. %H A141305 Amiram Eldar, <a href="/A141305/b141305.txt">Table of n, a(n) for n = 1..10000</a> %H A141305 Caroline Lucheta, Eli Miller and Clifford Reiter, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/34-3/lucheta.pdf">Digraphs from Powers Modulo p</a>, Fibonacci Quarterly, Volume 34, Number 3, June-July 1996. See p. 9. %H A141305 Troy Vasiga and Jeffrey Shallit, <a href="http://dx.doi.org/10.1016/S0012-365X(03)00158-4">On the iteration of certain quadratic maps over GF(p)</a>, Discrete Mathematics, Volume 277, Issues 1-3, 28 February 2004, Pages 219-240. See p.9. %t A141305 Select[Range[10^4], PrimeQ[#] && PrimeQ[(q = (# - 1)/2)] && PrimitiveRoot[q] == 2 &] (* _Amiram Eldar_, Oct 09 2021 *) %o A141305 (PARI) isok(p) = isprime(p) && (p%2) && isprime(q=(p-1)/2) && (q%2) && (znorder(Mod(2, q))==(q-1)); \\ _Michel Marcus_, Jan 30 2016 %Y A141305 Cf. A001122, A005385, A037178. %K A141305 nonn %O A141305 1,1 %A A141305 _T. D. Noe_, Jun 24 2008 %E A141305 Incorrect term 5 removed by _Michel Marcus_, Jan 30 2016