Search: id:A084742
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%I A084742
%S A084742 3,3,3,5,3,3,0,3,5,5,5,3,7,3,3,7,3,17,5,3,3,11,7,3,11,0,3,7,139,109,0,
               5,
%T A084742 3,11,31,5,5,3,53,17,3,5,7,103,7,5,5,7,1153,3,7,21943,7,3,37,53,3,17,3,
%U A084742 7,11,3,0,19,7,3,757,11,3,5,3,7,13,5,3,37,3,3,5,3,293,19,7,167,7,7,709
%N A084742 Least k such that (n^k+1)/(n+1) is prime, or 0 if no such prime exists.
%C A084742 Conjecture: No entry is zero.
%C A084742 a(8)>1000 - Michel ten Voorde (seqfan(AT)tenvoorde.org) Jun 20 2003
%C A084742 When (n^k+1)/(n+1) is prime, k must be prime. As mentioned by Dubner 
               and Granlund, when n is a power (greater than 2) of a prime, then 
               (n^k+1)/(n+1) will usually be composite for all k, which is the case 
               for n = 8, 27, 32 and 64. Some terms are only probable primes.
%H A084742 H. Dubner and T. Granlund, <a href="http://www.cs.uwaterloo.ca/journals/
               JIS/index.html">Primes of the Form (b^n+1)/(b+1)</a>, J. Integer 
               Sequences, 3 (2000), #P00.2.7.
%H A084742 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Repunit.html">Repunit</a>
%e A084742 a(7)= 3 as (7^3 +1 )/(7+1) = 1 - 7 + 7^2 =43 is a prime.
%Y A084742 Cf. A084741.
%Y A084742 Cf. A065507 (for p=prime(n), the least prime q such that (p^q+1)/(p+1) 
               is prime).
%Y A084742 Sequence in context: A108688 A123371 A011277 this_sequence A049613 A002373 
               A103153
%Y A084742 Adjacent sequences: A084739 A084740 A084741 this_sequence A084743 A084744 
               A084745
%K A084742 nonn
%O A084742 2,1
%A A084742 Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), 
               Jun 15 2003
%E A084742 More terms from T. D. Noe (noe(AT)sspectra.com), Jan 22 2004

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