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 A122197 Fractal sequence: count up to successive integers twice. 4

%I

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

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

%U 5,6,7,8,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5

%N Fractal sequence: count up to successive integers twice.

%C Fractal - deleting the first occurrence of each integer leaves the original sequence. Also, deleting the all 1's leaves the original sequence plus 1. New values occur at square indices. 1's occur at indices m^2+1 and m^2+m+1. Ordinal transform of A122196.

%C Except for its initial 1, A122197 is the natural fractal sequence of A002620; that is, A122197(n+1) is the number of the row of A194061 that contains n. See A194029 for definition of natural fractal sequence. [From Clark Kimberling, Aug 12 2011]

%H _Reinhard Zumkeller_, <a href="/A122197/b122197.txt">Table of n, a(n) for n = 1..10000</a>

%e 1, 1, 1,2, 1,2, 1,2,3, 1,2,3, etc.

%t With[{c=Table[Range[n],{n,10}]},Flatten[Riffle[c,c]]] (* _Harvey P. Dale_, Apr 19 2013 *)

%o a122197 n = a122197_list !! (n-1)

%o a122197_list = concat \$ zipWith (++) a002260_tabl a002260_tabl

%o -- _Reinhard Zumkeller_, Jul 19 2012

%Y Cf. A122196, A000290, A033638, A002260.

%K easy,nonn

%O 1,4

%A _Franklin T. Adams-Watters_, Aug 25 2006

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