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%I #60 Apr 18 2024 13:29:32
%S 0,1,3,6,2,7,13,20,4,22,12,23,11,24,10,25,9,26,8,27,47,5,49,72,48,73,
%T 21,75,19,77,17,79,15,81,115,45,117,43,119,41,121,39,123,37,125,35,
%U 127,33,129,31,131,29,133,80,134,189,245,74,16,193,253,70,132,69,197,67,199,65
%N a(0)=0; thereafter a(n) = the smallest nonnegative integer not already in the sequence such that a(n-1) is congruent to a(n) (mod n).
%C This sequence seems likely to be a permutation of the nonnegative integers.
%C A245340(n) = smallest m such that a(m) = n, or -1 if n never appears; see A245394 and A245395 for record values and where they occur. - _Reinhard Zumkeller_, Jul 21 2014
%C A very nice (maybe the most natural) variant of Recamán's sequence A005132. - _M. F. Hasler_, Nov 03 2014
%H Reinhard Zumkeller, <a href="/A125717/b125717.txt">Table of n, a(n) for n = 0..100000</a> (first 10000 terms from Ferenc Adorján)
%H Ferenc Adorján, <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).
%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t f[l_List] := Block[{n = Length[l], k = Mod[l[[ -1]], n]},While[MemberQ[l, k], k += n];Append[l, k]];Nest[f, {0}, 70] (* _Ray Chandler_, Feb 04 2007, updated for change to offset Oct 10 2019 *)
%o (PARI) {Quet_p2(n)=/* Permutation sequence a'la _Leroy Quet_, A125717 */local(x=[1],k=0,w=1); for(i=2,n,if((k=x[i-1]%i)==0,k=i);while(bittest(w,k-1)>0,k+=i);x=concat(x,k);w+=2^(k-1)); return(x)} [Ferenc Adorjan]
%o (Haskell)
%o import Data.IntMap (singleton, member, (!), insert)
%o a125717 n = a125717_list !! n
%o a125717_list = 0 : f [1..] 0 (singleton 0 0) where
%o f (v:vs) w m = 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 x : f vs x (insert x v m)
%o -- _Reinhard Zumkeller_, Jul 21 2014
%o (PARI) A125717(n,show=0)={my(u=1,a);for(n=1,n,a%=n;while(bittest(u,a),a+=n);u+=1<<a;show&&print1(a","));a} \\ _M. F. Hasler_, Nov 03 2014
%o (Python)
%o from itertools import count, islice
%o def agen(): # generator of terms
%o an, aset = 0, {0}
%o for n in count(1):
%o yield an
%o an = next(m for m in count(an%n, n) if m not in aset)
%o aset.add(an)
%o print(list(islice(agen(), 70))) # _Michael S. Branicky_, Jun 07 2023
%Y Cf. A005132, A099506.
%Y Cf. A125715, A125718, A125725.
%Y Cf. A245340, A245394, A245395.
%Y See also A370957 (first differences).
%K nonn,nice,look,changed
%O 0,3
%A _Leroy Quet_, Feb 01 2007
%E Extended by _Ray Chandler_, Feb 04 2007
%E a(0) added by _Franklin T. Adams-Watters_, Mar 31 2014
%E Edited by _N. J. A. Sloane_, Mar 15 2024
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