A131644 - OEIS

%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