A131644 a(n) = 2^(a(n-1)) mod n.

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, 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, 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

Offset

1,3

Comments

All positive integers seem to occur somewhere in this sequence (a proof would be nice!).

The first occurrence of 6 is at a(59474).

The first occurrence of 33 is at a(2514233).

a(A192362(n)) = n and a(m) <> n for m < A192362(n). - Reinhard Zumkeller, Jun 30 2011

The first occurrence of 75 is at a(8654593). - Reinhard Zumkeller, Jan 30 2015

Links

N. J. A. Sloane and T. D. Noe, Table of n, a(n) for n = 1..60000 (the first 1000 terms from T. D. Noe)

Formula

a(n) = 2^(a(n-1)) mod n, a(1) = 0

Example

a(11) = 4, so a(12) = 2^a(11) mod 12 = 16 mod 12 = 4.

Mathematica

Transpose[NestList[{Mod[2^First[#], Last[#]+1], Last[#]+1}&, {0, 1}, 95]][[1]]  (* Harvey P. Dale, Apr 17 2011 *)
Join[{s=0}, Table[s = PowerMod[2, s, n], {n, 2, 100}]] (* T. D. Noe, Apr 17 2011 *)

Prog

(Haskell)
import Math.NumberTheory.Moduli (powerMod)
a131644 n = a131644_list !! (n-1)
a131644_list = map fst $ iterate f (0, 2) where
   f (v, w) = (powerMod 2 v w, w + 1)
-- Reinhard Zumkeller, Jan 30 2015

Crossrefs

For records see A241582, A241583, also A192362.

Sequence in context: A368724 A304784 A354665 * A115346 A140531 A117316

Adjacent sequences: A131641 A131642 A131643 * A131645 A131646 A131647

Keyword

easy,nonn,nice

Author

Jon Ayres (jonathan.ayres(AT)ntlworld.com), Sep 08 2007

Status

approved