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%I #12 Nov 13 2023 17:53:44
%S 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 589,14,690,15,799,16,916,17,1009,19,1175,20,1316,21,1465,22,1622,23,
%U 1787,24,1960,25,2141,26,2330,27,2527,28,2732,29,2945,30,3166,31
%N 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 To build the sequence:
%C - we start with a(0) = 0, and repeatedly:
%C - let a(n) be the last known term and v the least value not yet in the sequence,
%C - if a(n) and v are congruent modulo n+1 then a(n+1) = v,
%C - 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 This construction is similar to that of A352713.
%C This sequence is a variant of A125717 and, by design, is guaranteed to be a permutation of the nonnegative integers (with inverse A367289).
%H Rémy Sigrist, <a href="/A367288/b367288.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A367288/a367288.gp.txt">PARI program</a>
%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>
%e The first terms are:
%e n a(n) a(n-1) mod n a(n) mod n
%e -- ---- ------------ ----------
%e 0 0 N/A N/A
%e 1 1 0 0
%e 2 5 1 1
%e 3 2 2 2
%e 4 18 2 2
%e 5 3 3 3
%e 6 39 3 3
%e 7 4 4 4
%e 8 60 4 4
%e 9 6 6 6
%e 10 106 6 6
%e 11 7 7 7
%e 12 151 7 7
%e 13 8 8 8
%o (PARI) See Links section.
%Y Cf. A005132, A125717, A352713, A367289 (inverse), A367290.
%K nonn
%O 0,3
%A _Rémy Sigrist_, Nov 12 2023
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