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%I #25 Jan 30 2015 19:49:31
%S 0,1,2,0,1,2,4,0,1,2,4,4,3,8,1,2,4,16,5,12,1,2,4,16,11,20,4,16,25,2,4,
%T 16,31,26,4,16,9,18,25,32,37,2,4,16,16,32,42,16,23,8,1,2,4,16,31,16,
%U 43,56,15,8,12,4,16,0,1,2,4,16,55,58,29,32,32,44,16,24,71,20,9,32,49,20,37
%N a(n) = 2^(a(n-1)) mod n.
%C All positive integers seem to occur somewhere in this sequence (a proof would be nice!).
%C The first occurrence of 6 is at a(59474).
%C The first occurrence of 33 is at a(2514233).
%C a(A192362(n)) = n and a(m) <> n for m < A192362(n). - _Reinhard Zumkeller_, Jun 30 2011
%C The first occurrence of 75 is at a(8654593). - _Reinhard Zumkeller_, Jan 30 2015
%H N. J. A. Sloane and T. D. Noe, <a href="/A131644/b131644.txt">Table of n, a(n) for n = 1..60000</a> (the first 1000 terms from T. D. Noe)
%F a(n) = 2^(a(n-1)) mod n, a(1) = 0
%e a(11) = 4, so a(12) = 2^a(11) mod 12 = 16 mod 12 = 4.
%t Transpose[NestList[{Mod[2^First[#],Last[#]+1],Last[#]+1}&,{0,1}, 95]][[1]] (* _Harvey P. Dale_, Apr 17 2011 *)
%t Join[{s=0}, Table[s = PowerMod[2, s, n], {n, 2, 100}]] (* _T. D. Noe_, Apr 17 2011 *)
%o (Haskell)
%o import Math.NumberTheory.Moduli (powerMod)
%o a131644 n = a131644_list !! (n-1)
%o a131644_list = map fst $ iterate f (0, 2) where
%o f (v, w) = (powerMod 2 v w, w + 1)
%o -- _Reinhard Zumkeller_, Jan 30 2015
%Y For records see A241582, A241583, also A192362.
%K easy,nonn,nice
%O 1,3
%A Jon Ayres (jonathan.ayres(AT)ntlworld.com), Sep 08 2007
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