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%I #22 Apr 18 2024 13:27:52
%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="/A245340/a245340.jpg">Log-log plot of A370959 vs A370956</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,changed
%O 0,3
%A _Reinhard Zumkeller_, Jul 21 2014
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