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A087088 If all the 1's are removed the sequence is the same as the original with every term one greater than before. It is the simplest nontrivial sequence with this property. 2

%I

%S 1,2,3,1,4,2,1,5,3,1,2,6,1,4,2,1,3,7,1,2,5,1,3,2,1,4,8,1,2,3,1,6,2,1,

%T 4,3,1,2,5,1,9,2,1,3,4,1,2,7,1,3,2,1,5,4,1,2,3,1,6,2,1,10,3,1,2,4,1,5,

%U 2,1,3,8,1,2,4,1,3,2,1,6,5,1,2,3,1,4,2,1,7,3,1,2,11,1,4,2,1,3,5,1,2,6,1,3,2

%N If all the 1's are removed the sequence is the same as the original with every term one greater than before. It is the simplest nontrivial sequence with this property.

%C From _Benoit Cloitre_, Mar 07 2009: (Start)

%C To construct the sequence:

%C Step 1: start from a sequence of 1 and leave 2 undefined places between two 1 giving: 1,(),(),1,(),(),1,(),(),1,(),(),1,(),(),1,...

%C Step 2: replace the first undefined place with a 2 and leave 2 undefined places between two 2 giving: 1,2,(),1,(),2,1,(),(),1,2,(),1,(),2,1,...

%C Step 3: replace the first undefined place with a 3 and leave 2 undefined places between two 3 giving: 1,2,3,1,(),2,1,(),3,1,2,(),1,(),2,1,...

%C Step 4: replace the first undefined place with a 4 and leave 2 undefined places between two 4 giving: 1,2,3,1,4,2,1,(),3,1,2,(),1,4,2,1,... Iterating the process indefinitely yields the sequence: 1,2,3,1,4,2,1,5,3,1,2,6,1,4,2,1,... (End)

%H Alois P. Heinz, <a href="/A087088/b087088.txt">Table of n, a(n) for n = 3..10000</a>

%F a(n) = 1 when n == 1 (mod 3), otherwise a(n) = a(n-ceiling(n/3)) + 1.

%F a(n) = 3 + A244040(3*(n-1)) - A244040(3*n). - _Tom Edgar_ and _James Van Alstine_, Aug 04 2014

%Y Cf. A001511, A244040.

%Y Records are given by A061419: a(A061419(n))=n, where A061419(n) = ceiling(A061419(n-1)*3/2).

%K nonn,easy

%O 3,2

%A Enrico T. Federighi (rico125162(AT)aol.com), Aug 08 2003

%E More terms from _Paul D. Hanna_, Aug 21 2003

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Last modified August 19 18:33 EDT 2019. Contains 326133 sequences. (Running on oeis4.)