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1+A053735(n-1), where A053735 is the sum-of-digits function in base 3.
7

%I #16 Mar 30 2012 17:34:04

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

%T 5,6,3,4,5,4,5,6,5,6,7,4,5,6,5,6,7,6,7,8,3,4,5,4,5,6,5,6,7,4,5,6,5,6,

%U 7,6,7,8,5,6,7,6,7,8,7,8,9,2,3,4,3,4,5,4,5,6,3,4,5,4,5,6,5,6,7,4,5,6,5,6,7,6,7,8,3,4,5,4,5,6,5,6,7,4,5,6

%N 1+A053735(n-1), where A053735 is the sum-of-digits function in base 3.

%C A053735 can be obtained as 0 followed by the first 2 terms of this sequence, followed by the first 6 terms, followed by the first 18 terms, ..., followed by the first 2*3^n terms, etc.

%C Similar observations are possible for: A063787 (base-2 case), and generic comments have been gathered in A173525 (base-5 case).

%C Fixed point of morphism 1->123, 2->234, 3->345 etc. (start with 1).

%e If written as a triangle, begins:

%e 1,

%e 2,3,

%e 2,3,4,3,4,5,

%e 2,3,4,3,4,5,4,5,6,3,4,5,4,5,6,5,6,7,

%e 2,3,4,3,4,5,4,5,6,3,4,5,4,5,6,5,6,7,4,5,6,5,6,7,6,7,8,...

%Y Cf. A000120, A053735, A063787, A173524 - A173529.

%K base,nonn

%O 1,2

%A _Omar E. Pol_, Feb 20 2010