cp's OEIS Frontend

A363757 Lexicographically earliest sequence of positive integers such that the n-th pair of consecutive equal values are separated by a(n) distinct terms, with pairs numbered according to the position of the second term in the pair.

%I A363757 #78 Jul 21 2023 09:15:42
%S A363757 1,2,1,3,2,3,4,1,3,2,5,4,5,3,4,6,1,5,2,6,4,7,3,7,5,3,1,4,8,2,1,6,3,2,
%T A363757 3,8,9,7,8,7,1,9,7,8,5,10,4,3,2,9,2,6,8,7,3,11,1,8,3,1,10,3,6,9,7,3,
%U A363757 12,5,12,8,3,8,2,12,9,1,7,12,13,4,9,11,8,4,2,8,10,1,10,13,6
%N A363757 Lexicographically earliest sequence of positive integers such that the n-th pair of consecutive equal values are separated by a(n) distinct terms, with pairs numbered according to the position of the second term in the pair.
%C A363757 The word 'distinct' differentiates this sequence from A363654.
%C A363757 A000124 gives the index of the first occurrence of n, and A080036 gives the indices of the remaining terms. A record high term occurs when its corresponding pair number would be the previous record high, since that would have to use all terms between the enclosing pair, which is impossible.
%C A363757 A083920(n) gives the number of pairs in the first n terms of this sequence.
%C A363757 If pairs are numbered according to the position of the first term in the pair (rather than second), this becomes A001511 (the ruler function).
%H A363757 Neal Gersh Tolunsky, <a href="/A363757/b363757.txt">Table of n, a(n) for n = 1..10000</a>
%H A363757 Neal Gersh Tolunsky, <a href="/A363757/a363757.png">Graph of first 100000 terms</a>
%e A363757 The 1st pair (1,2,1) encloses 1 term because a(1)=1.
%e A363757 The 2nd pair (2,1,3,2) encloses 2 distinct terms because a(2)=2.
%e A363757 The 3rd pair (3,2,3) encloses 1 term because a(3)=1.
%e A363757 The 4th pair (1,3,2,3,4,1) encloses 3 distinct terms because a(4)=3.
%e A363757 a(4)=3 since if we place a 1 or a 2 (creating the second pair), this would enclose less than a(2)=2 distinct terms, so a(4) must be the smallest unused number, which is 3.
%Y A363757 Cf. A363654, A363708, A026272, A330896.
%K A363757 nonn
%O A363757 1,2
%A A363757 _Neal Gersh Tolunsky_, Jun 23 2023