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A367288 Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, a(n-1) and a(n) are congruent modulo n, and the least value not yet in the sequence appears as soon as possible.

%I A367288 #12 Nov 13 2023 17:53:44
%S A367288 0,1,5,2,18,3,39,4,60,6,106,7,151,8,204,9,265,10,334,11,411,12,496,13,
%T A367288 589,14,690,15,799,16,916,17,1009,19,1175,20,1316,21,1465,22,1622,23,
%U A367288 1787,24,1960,25,2141,26,2330,27,2527,28,2732,29,2945,30,3166,31
%N A367288 Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, a(n-1) and a(n) are congruent modulo n, and the least value not yet in the sequence appears as soon as possible.
%C A367288 To build the sequence:
%C A367288 - we start with a(0) = 0, and repeatedly:
%C A367288 - let a(n) be the last known term and v the least value not yet in the sequence,
%C A367288 - if a(n) and v are congruent modulo n+1 then a(n+1) = v,
%C A367288 - otherwise a(n+2) = v and a(n+1) is chosen as small as possible in such a way as to satisfy the required congruences (this is always possible as n+1 and n+2 are coprime).
%C A367288 This construction is similar to that of A352713.
%C A367288 This sequence is a variant of A125717 and, by design, is guaranteed to be a permutation of the nonnegative integers (with inverse A367289).
%H A367288 Rémy Sigrist, <a href="/A367288/b367288.txt">Table of n, a(n) for n = 0..10000</a>
%H A367288 Rémy Sigrist, <a href="/A367288/a367288.gp.txt">PARI program</a>
%H A367288 <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>
%H A367288 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A367288 The first terms are:
%e A367288   n   a(n)  a(n-1) mod n  a(n) mod n
%e A367288   --  ----  ------------  ----------
%e A367288    0     0  N/A           N/A
%e A367288    1     1             0           0
%e A367288    2     5             1           1
%e A367288    3     2             2           2
%e A367288    4    18             2           2
%e A367288    5     3             3           3
%e A367288    6    39             3           3
%e A367288    7     4             4           4
%e A367288    8    60             4           4
%e A367288    9     6             6           6
%e A367288   10   106             6           6
%e A367288   11     7             7           7
%e A367288   12   151             7           7
%e A367288   13     8             8           8
%o A367288 (PARI) See Links section.
%Y A367288 Cf. A005132, A125717, A352713, A367289 (inverse), A367290.
%K A367288 nonn
%O A367288 0,3
%A A367288 _Rémy Sigrist_, Nov 12 2023