A245340 Smallest m such that A125717(m) = n, or -1 if n never appears.

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, 15, 17, 19, 102, 51, 100, 49, 98, 47, 96, 45, 94, 43, 92, 41, 90, 39, 88, 37, 86, 35, 84, 20, 24, 22, 505, 81, 2510, 79, 166, 77, 296, 75, 501, 73, 162, 71, 498, 69

Offset: 0

Author

Reinhard Zumkeller, Jul 21 2014

Keywords

• nonn

Comments

Conjecture: a(n) is never -1.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Ferenc Adorjan, Some characteristics of Leroy Quet's permutation sequences
• N. J. A. Sloane, Log-log plot of A370956 vs A370959 (shows terms in A125717 that take the longest to appear).

Crossrefs

Cf. A245394, A245395, A057167.

For RECORDS see A370956 and A370959.

Programs

Haskell

import Data.IntMap (singleton, member, (!), insert)
a245340 n = a245340_list !! n
a245340_list = 0 : f [1..] [1..] 0 (singleton 0 0) where
   f us'@(u:us) vs'@(v:vs) w m
     | u `member` m = (m ! u) : f us vs' w m
     | otherwise    = g (reverse[w-v,w-2*v..1] ++ [w+v,w+2*v..]) where
     g (x:xs) = if x `member` m then g xs else f us' vs x $ insert x v m

Python

from itertools import count
def A245340(n):
    a, aset = 0, set()
    for m in count(1):
        if a==n: return m-1
        aset.add(a)
        a = next(a for a in count(a%m,m) if a not in aset) # Chai Wah Wu, Mar 13 2024