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The successive numbers of integers visible between two even terms are given by the sequence itself.
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%I #4 Jun 02 2016 09:11:02

%S 0,2,1,3,4,5,6,7,9,11,8,13,15,17,19,10,21,23,25,27,29,12,31,33,35,37,

%T 39,41,14,43,45,47,49,51,53,55,16,57,59,61,63,65,67,69,71,73,18,75,77,

%U 79,81,83,85,87,89,91,93,95,20,97,99,101,103,105,107,109,111,22,113,115,117,119,121,123,125,127,129,131,133,135,137,24,139,141,143,145,147,149,151,153,155,157,159,161,163,165,167,26

%N The successive numbers of integers visible between two even terms are given by the sequence itself.

%C The sequence starts with a(1)=0. It is then extended with the smallest integer not yet present and not leading to a contradiction. The sequence is a permutation of the integers >=0.

%e The first two even terms that appear in the sequence are 0 and 2; between 0 and 2 there are 0 integers and this 0 corresponds to the starting 0 of the sequence.

%e The next even term is 4 and between 2 and 4 there are 2 integers [which are 1 and 3] and this 2 corresponds to the next term of the sequence.

%e The next even term is 6 and between 4 and 6 there is 1 integer [which is 5] and this 1 corresponds to the next term of the sequence.

%e The next even term is 8 and between 6 and 8 there are 3 integers [which are 7, 9 and 11] and this 3 corresponds to the next term of the sequence.

%e The next even term is 10 and between 8 and 10 there are 4 integers [which are 13, 15, 17 and 19] and this 4 corresponds to the next term of the sequence.

%e Etc.

%K nonn,base

%O 1,2

%A _Eric Angelini_, Jun 01 2016