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This sequence displays every positive integer exactly three times; there is one number between the first and second 1's and one number between the second and third 1's; two numbers between the first and second 2's and two numbers between the second and third 2's; ... n numbers between the first and second n's and n numbers between the second and third n's.
1

%I #9 Nov 13 2018 00:36:41

%S 1,3,1,4,1,3,5,6,4,3,8,10,5,4,6,7,9,11,5,8,13,6,10,7,2,12,9,2,8,11,2,

%T 7,14,10,13,16,9,17,12,18,15,11,20,21,22,24,19,14,13,25,23,12,16,26,

%U 27,17,15,30,18,31,28,32,14,20,34,21,19,22,33,16,24,36,15,17,23,25,35,18,37

%N This sequence displays every positive integer exactly three times; there is one number between the first and second 1's and one number between the second and third 1's; two numbers between the first and second 2's and two numbers between the second and third 2's; ... n numbers between the first and second n's and n numbers between the second and third n's.

%C The sequence displaying every positive integer exactly twice is A026272. Construction method: we always fill the next empty "hole" with the smallest available integer. There is no proof that this sequence could go on forever. Terms computed by Gilles Sadowski.

%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Kimberlike02.htm">Kimberlike sequences</a>

%H E. Angelini, <a href="/A143825/a143825.pdf">Kimberlike sequences</a> [Cached, with permission]

%K base,nonn

%O 1,2

%A _Eric Angelini_, Sep 02 2008