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Summarize the previous term in binary (in increasing order).
2

%I #3 Mar 30 2012 17:36:43

%S 1,11,101,10101,100111,1001001,1000111,1101001,1101001,1101001,

%T 1101001,1101001,1101001,1101001,1101001,1101001,1101001,1101001,

%U 1101001,1101001,1101001,1101001,1101001,1101001,1101001,1101001,1101001

%N Summarize the previous term in binary (in increasing order).

%C Similar to A005151 but uses base 2: Let a(1)=1. Describing a(1) as "one 1" again gives a(2)=11 (same digit string as A005151 and similar sequences), but describing a(2) as "two 1's" gives a(3)=101 when the frequency of digit occurrence is written in binary and followed by the digit counted.

%F a(n) = 1101001 for all n >= 8 (see example).

%e Summarizing a(8) = 1101001 in increasing digit order, there are "three 0's, four 1's", so concatenating 11 0 100 1 gives a(9) = 1101001 (=a(10)=a(11)=...).

%Y Cf. A098154 (ternary), A098155 (base 4), A005151 (decimal and digit strings for all other bases b >= 5).

%K base,easy,nonn

%O 1,2

%A _Rick L. Shepherd_, Aug 29 2004