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Smallest natural number requiring n applications of the map x -> 2^x mod x = A015910(x) to reach 0.
1

%I #33 Sep 22 2024 07:24:31

%S 0,1,3,18,35,207,774,1513,2051,8900,13459,25907,34305,88036,153839,

%T 382283,397590,636459,844177,1456073,2426735,7312307,11716125,

%U 14657311,43165242,52706549,84955821,188736643,416569989,953350161,1617152961,2541237149,4847485412

%N Smallest natural number requiring n applications of the map x -> 2^x mod x = A015910(x) to reach 0.

%C A015910 is conjectured to contain every natural number except for 1, which would imply that this sequence has infinitely many terms.

%H Kevin Ryde, <a href="/A372707/b372707.txt">Table of n, a(n) for n = 0..45</a>

%H Kevin Ryde, <a href="/A372707/a372707.c.txt">C Code</a>

%o (Python)

%o i = 0

%o c = [0]

%o for j in range(10**9):

%o if c[-1] == i:

%o print(f"a({i}) = {j}")

%o i += 1

%o c.append(1+c[pow(2, len(c), len(c))])

%o (C) /* See links. */

%Y Cf. A015910.

%K nonn

%O 0,3

%A _Bryle Morga_, May 11 2024

%E a(30)-a(32) from _Michael S. Branicky_, May 12 2024