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 A084740 #119 Feb 16 2025 08:32:49
%S A084740 2,3,2,3,2,5,3,0,2,17,2,5,3,3,2,3,2,19,3,3,2,5,3,0,7,3,2,5,2,7,0,3,13,
%T A084740 313,2,13,3,349,2,3,2,5,5,19,2,127,19,0,3,4229,2,11,3,17,7,3,2,3,2,7,
%U A084740 3,5,0,19,2,19,5,3,2,3,2,5,5,3,41,3,2,5,3,0,2,5,17,5,11,7,2,3,3,4421,439,7,5,7,2,17,13,3,2,3,2,19,97,3,2,17,2,17,3,3,2,23,29,7,59
%N A084740 Least k such that (n^k-1)/(n-1) is prime, or 0 if no such prime exists.
%C A084740 When (n^k-1)/(n-1) is prime, k must be prime. As mentioned by Dubner, when n is a perfect power, then (n^k-1)/(n-1) will usually be composite for all k, which is the case for n = 9, 25, 32, 49, 64, 81, 121, 125, 144, 169, 216, 225, 243, 289, 324, 343, ... - _T. D. Noe_, Jan 30 2004
%C A084740 a(152) > prime(1100) or 0. - _Derek Orr_, Nov 29 2014
%C A084740 a(n)=2 if and only if n=p-1, where p is an odd prime; that is, n belongs to A006093, except 2. - _Thomas Ordowski_, Sep 19 2015
%C A084740 Probably a(152) = 270217 since (152^270217-1)/(152-1) has been shown to be probably prime. - _Michael Stocker_, Jan 24 2019
%H A084740 Eric Chen, <a href="/A084740/a084740_2.txt">Table of known a(n) up to a(360)</a> [with a(316) corrected by Jon E. Schoenfield]
%H A084740 H. Dubner, <a href="http://dx.doi.org/10.1090/S0025-5718-1993-1185243-9">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930.
%H A084740 Andy Steward, <a href="http://www.users.globalnet.co.uk/~aads/titans.html">Titanic Prime Generalized Repunits</a>
%H A084740 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>
%H A084740 Robert G. Wilson v, <a href="/A084740/a084740.pdf">Letter to N. J. A. Sloane, circa 1991.</a>
%H A084740 Robert G. Wilson v, <a href="/A084740/a084740_4.txt">Table of known a(n) from n = 2 to 1000.</a>
%e A084740 a(7) = 5 as (7^5 - 1 )/(7 - 1) = 2801 = 1 + 7 + 7^2 + 7^3 + 7^4 is a prime but no smaller partial sum yields a prime.
%o A084740 (PARI) a(n) = {l=List([9, 25, 32, 49, 64, 81, 121, 125, 144, 169, 216, 225, 243, 289, 324, 343]); for(q=1, #l, if(n==l[q], return(0))); k=1; while(k, s=(n^prime(k)-1)/(n-1); if(ispseudoprime(s), return(prime(k))); k++)}
%o A084740 n=2; while(n<361, print1(a(n), ", "); n++) \\ _Derek Orr_, Jul 13 2014
%Y A084740 Cf. A065507, A065854, A084738, A084742, A096059, A126659, A128164, A246005.
%Y A084740 Cf. A066180, A085398, A103795, A123487, A123627.
%K A084740 nonn
%O A084740 2,1
%A A084740 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003
%E A084740 More terms from _T. D. Noe_, Jan 23 2004