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A125715 a(1)=1. a(n) = the smallest positive integer not occurring earlier in the sequence such that (sum{k=1 to n-1} a(k)) is congruent to a(n) (mod n).

%I A125715 #16 Oct 10 2019 15:53:51
%S A125715 1,3,4,8,6,10,11,19,17,9,22,2,21,7,5,33,25,23,36,42,31,27,40,18,20,24,
%T A125715 32,48,51,55,30,72,26,64,37,15,43,63,103,143,16,44,59,45,60,90,56,80,
%U A125715 79,75,14,96,52,68,100,108,65,91,84,128,94,146,61,13,110,176,107,99,12,114
%N A125715 a(1)=1. a(n) = the smallest positive integer not occurring earlier in the sequence such that (sum{k=1 to n-1} a(k)) is congruent to a(n) (mod n).
%C A125715 This sequence seems likely to be a permutation of the positive integers.
%H A125715 Ferenc Adorjan, <a href="/A125715/b125715.txt">Table of n,a(n) for n=1,10000</a>
%H A125715 Ferenc Adorjan, <a href="http://web.t-online.hu/fadorjan/l_quet.pdf">Some characteristics of _Leroy Quet_'s permutation sequences</a>
%t A125715 f[l_List] := Block[{n = Length[l] + 1, k = Mod[Plus @@ l, n, 1]},While[MemberQ[l, k], k += n];Append[l, k]];Nest[f, {1}, 70] (* _Ray Chandler_, Feb 04 2007 *)
%o A125715 (PARI) {Quet_p1(n)=/* Permutation sequence a'la _Leroy Quet_, A125715 */local(x=[1],s=1,k=0,w=1); for(i=2,n,if((k=s%i)==0,k=i);while(bittest(w,k-1)>0,k+=i);x=concat(x,k);s+=k;w+=2^(k-1));return(x)}
%K A125715 nonn
%O A125715 1,2
%A A125715 _Leroy Quet_, Feb 01 2007
%E A125715 Extended by _Ray Chandler_, Feb 04 2007