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%I #11 Nov 13 2023 17:50:30
%S 1,5,2,17,3,69,4,310,6,558,7,193,8,869,9,2077,10,1780,11,3562,12,961,
%T 13,6155,14,2439,15,8255,16,6120,18,12464,19,9472,20,11195,21,4260,22,
%U 24070,23,16133,24,18360,25,19528,26,27456,27,25905,28,46395,29,6054
%N Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(n) and a(n+1) are congruent modulo the n-th prime number, and the least value not yet in the sequence appears as soon as possible.
%C To build the sequence:
%C - we start with a(1) = 1, 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 the n-th prime number 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 two consecutive prime numbers are coprime).
%C This sequence is a variant of A364054, and, by design, is guaranteed to be a permutation of the positive integers (with inverse A367291).
%H Rémy Sigrist, <a href="/A367290/b367290.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A367290/a367290.gp.txt">PARI program</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) mod prime(n) a(n+1) mod prime(n)
%e -- ----- ----------------- -------------------
%e 1 1 1 1
%e 2 5 2 2
%e 3 2 2 2
%e 4 17 3 3
%e 5 3 3 3
%e 6 69 4 4
%e 7 4 4 4
%e 8 310 6 6
%e 9 6 6 6
%e 10 558 7 7
%e 11 7 7 7
%e 12 193 8 8
%e 13 8 8 8
%o (PARI) See Links section.
%Y Cf. A364054, A367288, A367291 (inverse).
%K nonn
%O 1,2
%A _Rémy Sigrist_, Nov 12 2023
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