cp's OEIS Frontend

A369852 a(1)=1, a(2)=2; thereafter, any two indices n with different a(n) values reach distinct values by a single jump, where jumps are allowed from location i to i+a(i).

%I A369852 #44 Mar 02 2024 06:28:12
%S A369852 1,2,2,3,1,2,4,1,5,2,6,1,2,7,1,2,8,1,5,2,9,1,5,7,10,1,2,11,3,12,9,4,1,
%T A369852 13,14,15,1,5,16,12,3,17,7,4,1,18,19,6,20,21,22,23,3,8,24,4,1,5,25,26,
%U A369852 4,10,7,27,15,28,1,13,29,30,31,32,33,2,34,1,5,5
%N A369852 a(1)=1, a(2)=2; thereafter, any two indices n with different a(n) values reach distinct values by a single jump, where jumps are allowed from location i to i+a(i).
%C A369852 Consider each index i as a location from which one can jump a(i) terms forward. To find a(n) we have to check 2 conditions:
%C A369852 1. The value a(n) can be reached in one jump by at most one distinct value.
%C A369852 2. Location n reaches a location in one jump that is not reached in one jump from a location before n.
%C A369852 Another way to view the sequence is to consider the sets of values that can be reached from each distinct integer by a single jump forward (values reached by 1s in the sequence, values reached by 2s, 3s etc.): all of these sets are disjoint.
%H A369852 Neal Gersh Tolunsky, <a href="/A369852/b369852.txt">Table of n, a(n) for n = 1..10000</a>
%e A369852 a(4)=3 because:
%e A369852   a(4) cannot be 1 because then we would have two distinct values (a(3)=2, a(4)=1) that reach the same future value a(5)=x:
%e A369852   1, 2, 2, 1, x
%e A369852         2---->x
%e A369852            1->x
%e A369852   a(4) cannot be 2 because then we would have two distinct values (a(1)=1, a(2)=2) reach the same value 2:
%e A369852   1, 2, 2, 2
%e A369852   1->2
%e A369852      2---->2
%e A369852   a(4) can be 3 without contradiction since there is only one distinct value that can reach the value 3 (a(2)=2):
%e A369852   1, 2, 2, 3
%e A369852      2---->3
%t A369852 lst={1,2};Do[z=1;Quiet@While[l=Join[lst,{z}]; Union[Length@*Union/@ GatherBy[Select[Table[{l[[k]],l[[l[[k]]+k]]},{k,Length@l}],IntegerQ@Last@#&],Last]]!={1}||
%t A369852 MemberQ[Table[l[[k]]+k,{k,Length@l-1}],Length@l+Last@l],z++];AppendTo[lst,z],{i,89}];lst (* _Giorgos Kalogeropoulos_, Feb 29 2024 *)
%Y A369852 Cf. A369475, A368485, A367849, A367832, A367467.
%K A369852 nonn
%O A369852 1,2
%A A369852 _Neal Gersh Tolunsky_, Feb 06 2024
%E A369852 More terms from _Giorgos Kalogeropoulos_, Feb 28 2024