A245340 - OEIS

%I #24 Apr 30 2024 16:28:32

%S 0,1,4,2,8,21,3,5,18,16,14,12,10,6,1518,32,58,30,184,28,7,26,9,11,13,

%T 15,17,19,102,51,100,49,98,47,96,45,94,43,92,41,90,39,88,37,86,35,84,

%U 20,24,22,505,81,2510,79,166,77,296,75,501,73,162,71,498,69

%N Smallest m such that A125717(m) = n, or -1 if n never appears.

%C Conjecture: a(n) is never -1.

%H Reinhard Zumkeller, <a href="/A245340/b245340.txt">Table of n, a(n) for n = 0..10000</a>

%H Ferenc Adorjan, <a href="https://web.archive.org/web/20210629063154/http://web.t-online.hu/fadorjan/l_quet.pdf">Some characteristics of Leroy Quet's permutation sequences</a>

%H N. J. A. Sloane, <a href="/A125717/a125717.jpg">Log-log plot of A370956 vs A370959</a> (shows terms in A125717 that take the longest to appear).

%o (Haskell)

%o import Data.IntMap (singleton, member, (!), insert)

%o a245340 n = a245340_list !! n

%o a245340_list = 0 : f [1..] [1..] 0 (singleton 0 0) where

%o    f us'@(u:us) vs'@(v:vs) w m

%o      | u `member` m = (m ! u) : f us vs' w m

%o      | otherwise    = g (reverse[w-v,w-2*v..1] ++ [w+v,w+2*v..]) where

%o      g (x:xs) = if x `member` m then g xs else f us' vs x $ insert x v m

%o (Python)

%o from itertools import count

%o def A245340(n):

%o     a, aset = 0, set()

%o     for m in count(1):

%o         if a==n: return m-1

%o         aset.add(a)

%o         a = next(a for a in count(a%m,m) if a not in aset) # _Chai Wah Wu_, Mar 13 2024

%Y Cf. A245394, A245395, A057167.

%Y For RECORDS see A370956 and A370959.

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, Jul 21 2014