Search: id:A005105
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%I A005105 M0665
%S A005105 2,3,5,7,11,17,23,31,47,53,71,107,127,191,383,431,647,863,971,1151,2591,
%T A005105 4373,6143,6911,8191,8747,13121,15551,23327,27647,62207,73727,131071,
%U A005105 139967,165887,294911,314927,442367,472391,497663,524287,786431,995327
%N A005105 Primes of the form 2^i*3^j - 1 with i, j >= 0.
%C A005105 Class 1+ primes.
%C A005105 Odd terms are primes satisfying p==-1 (mod phi(p+1)). - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Feb 22 2002
%D A005105 G. Everest, P. Rogers and T. Ward, A higher-rank Mersenne problem, pp. 
               95-107 of ANTS 2002, Lect. Notes Computer Sci. 2369 (2002).
%D A005105 R. K. Guy, Unsolved Problems in Number Theory, A18.
%D A005105 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005105 T. D. Noe, <a href="b005105.txt">Table of n, a(n) for n=1..691</a>
%H A005105 R. J. Mathar, <a href="a005105.txt">Maple programs to generate b-files 
               for b005105 to b005108, b081633 etc.</a>
%p A005105 For Maple program see Mathar link.
%t A005105 Take[ Select[ Sort[ Flatten[ Table[2^t*3^u - 1, {t, 0, 22}, {u, 0, 16}]]], 
               PrimeQ[ # ] &], 43] (* or *)
%t A005105 Prime[ Select[ Range[78200], Mod[ Prime[ # ] + 1, EulerPhi[ Prime[ # 
               ] + 1]] == 0 &]] (* or *)
%t A005105 PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; 
               f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/
               2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] 
               + 1]]; ClassPlusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] 
               - 3; Prime[ Select[ Range[3, 78200], ClassPlusNbr[ Prime[ # ]] == 
               1 &]]
%Y A005105 Cf. A069353, A069356, A005109, A005113, A005106, A005107, A005108.
%Y A005105 Sequence in context: A040089 A113161 A038953 this_sequence A086566 A104892 
               A065436
%Y A005105 Adjacent sequences: A005102 A005103 A005104 this_sequence A005106 A005107 
               A005108
%K A005105 nonn
%O A005105 1,1
%A A005105 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A005105 More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 22 2002
%E A005105 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 20 
               2003

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