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 A254410 Limit of f(f(f(...f(2))...) modulo n as the number of iterations of f(x) = 2^x - 1 grows. 3
 0, 1, 1, 3, 2, 1, 1, 7, 1, 7, 6, 7, 10, 1, 7, 15, 8, 1, 1, 7, 1, 17, 17, 7, 2, 23, 1, 15, 26, 7, 3, 31, 28, 25, 22, 19, 34, 1, 10, 7, 4, 1, 1, 39, 37, 17, 35, 31, 1, 27, 25, 23, 32, 1, 17, 15, 1, 55, 36, 7, 5, 3, 1, 63, 62, 61, 43, 59, 40, 57, 49, 55, 1, 71, 52, 39, 50, 49, 75, 47, 1, 45, 66, 43, 42, 1, 55, 39, 63, 37, 36, 63, 34, 35, 77, 31, 65, 1, 28, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Also, limit of f(f(f(...f(m))...) modulo n for any integer m >= 2. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 FORMULA a(n) = limit of A007013(m) mod n as m grows. a(n) = A007013(A227944(n) + k) mod n for any k >= 1. In particular, a(n) = A007013(n) mod n. MATHEMATICA Clear[a]; Unprotect[Power]; 0^0 = 1; a[1]=0; a[n_] := a[n] = Module[{g, m = n}, g = 2^IntegerExponent[m, 2]; m = Floor[m/g]; Mod[ ChineseRemainder[ {0, Mod[2, m]^a[EulerPhi[m]]}, {g, m}] - 1, n]]; Array[a, 100] (* Jean-François Alcover, Jan 01 2016, adapted from PARI *) PROG (PARI) { A254410(m) = my(g); if(m==1, return(0)); g=2^valuation(m, 2); m\=g; lift( chinese(Mod(0, g), Mod(2, m)^A254410(eulerphi(m)) ) - 1) } CROSSREFS Cf. A245970, A254411. Sequence in context: A113185 A132069 A259786 * A073201 A118654 A111760 Adjacent sequences:  A254407 A254408 A254409 * A254411 A254412 A254413 KEYWORD nonn,easy,nice,look AUTHOR Max Alekseyev, Jan 30 2015 STATUS approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)