cp's OEIS Frontend

A369475 Lexicographically earliest infinite sequence such that, from all indices n with the same a(n) value, the terms reached by a single jump are all distinct, where jumps are allowed from location i to i+-a(i).

%I A369475 #21 Jan 25 2024 17:04:26
%S A369475 1,2,2,3,4,1,5,3,2,5,6,1,7,4,6,3,1,8,8,2,5,7,3,5,6,9,1,10,11,1,12,3,2,
%T A369475 3,10,4,13,1,14,6,2,3,9,5,15,7,2,9,13,7,5,4,4,4,6,10,12,11,9,2,10,16,
%U A369475 1,15,3,4,5,17,1,18,9,12,3,6,5,19,1,20,9,15
%N A369475 Lexicographically earliest infinite sequence such that, from all indices n with the same a(n) value, the terms reached by a single jump are all distinct, where jumps are allowed from location i to i+-a(i).
%C A369475 Consider each index i as a location from which one can jump a(i) terms forwards or backwards. From all indices with the same a(n) value, every jump is to a distinct term.
%C A369475 Another way to define the sequence is to consider every possible ordered pair of values of the form (origin value, destination value)--every such ordered pair is distinct.
%H A369475 Pontus von Brömssen, <a href="/A369475/b369475.txt">Table of n, a(n) for n = 1..10000</a>
%H A369475 Pontus von Brömssen, <a href="/A369475/a369475.png">Plot of (n,a(n)) for n = 1..1000000</a>.
%H A369475 Pontus von Brömssen, <a href="/A369475/a369475_1.png">Plot of (n, log(a(n))/log(n)) for n = 2..1000000</a>.
%e A369475 a(5)=4 because:
%e A369475 a(5) cannot be 1 because then we would have two jumps from a term with the same value 2, both landing on the value 1--ordered pair (2,1) twice:
%e A369475   1, 2, 2, 3, 1
%e A369475         2---->1
%e A369475   1<----2
%e A369475 a(5) cannot be 2 because we would have two jumps from the same a(n) value 2 to the same value 2--ordered pair (2,2) twice:
%e A369475   1, 2, 2, 3, 2
%e A369475         2---->2
%e A369475         2<----2
%e A369475 a(5) cannot be 3 because we would have two jumps from the same a(n) value 2 to the same a(n) value 3--ordered pair (2,3) twice:
%e A369475   1, 2, 2, 3, 3
%e A369475      2---->3
%e A369475         2---->3
%e A369475 a(5) can be 4 without contradiction.
%Y A369475 Cf. A368485, A367849, A367832, A367467.
%K A369475 nonn,look
%O A369475 1,2
%A A369475 _Neal Gersh Tolunsky_, Jan 23 2024
%E A369475 More terms from _Pontus von Brömssen_, Jan 24 2024