A132601 - OEIS

%I #4 Mar 30 2012 18:50:59

%S 1,2,1,5,1,2,7,14,18,16,2,1,3,7,1,6,40,46,20,20,7,62,13,31,80,8,12,6,

%T 20,4,23,111,76,9,4,132,15,9,9,20,20,18,48,134,71,45,39,3,51,13,4,10,

%U 9,31,71,34,2,8,71,25,78,56,178,280,184,106,8,185,8,276,44,5,7,12,143,24,18

%N Let S be the concatenation of natural numbers in binary representation: a(n) = position of first occurrence of n in S, then this occurrence in S is replaced by a(n) in binary.

%C A132602(n) = smallest m such that a(m) = n;

%C A132603 and A132604 give record values and where they occur;

%C A132605 gives numbers m such that a(m) = m;

%C A132606 gives positions m such that a(m)=a(m-1).

%H R. Zumkeller, <a href="/A132601/b132601.txt">Table of n, a(n) for n = 1..10000</a>

%e S(0) = 110111001011101111000100110101011 ..;

%e for n<=2: a(n)=n, S(n) = S(n-1);

%e n=3->'11', a(3)=1->'1', S(3)=10111001011101111000100110101011..;

%e n=4->'100', a(4)=5->'101', S(4)=10111011011101111000100110101011..;

%e n=5->'101', a(5)=1->'1', S(5)=111011011101111000100110101011..;

%e n=6->'110', a(6)=2->'10', S(6)=11011011101111000100110101011..;

%e n=7->'111', a(7)=7->'111', S(7)=S(6);

%e n=8->'1000', a(8)=14->'1110', S(8)=11011011101111110100110101011..;

%e n=9->'1001', a(9)=18->'10010', S(9)=110110111011111101001010101011..;

%e n=10->'1010', a(10)=16->'10000',

%e S(10)=1101101110111111000001010101011..;

%e n=11->'1011', a(11)=2->'10', S(11)=11001110111111000001010101011..;

%e n=12->'1100', a(12)=1->'1', S(12)=11110111111000001010101011..;

%e n=13->'1101', a(13)=3->'11', S(13)=111111111000001010101011..;

%e n=14->'1110', a(14)=7->'111', S(14)=11111111000001010101011..;

%e n=15->'1111', a(15)=1->'1', S(15)=111111000001010101011..;

%e n=16->'10000', a(16)=6->'110', S(16)=1111111001010101011.. .

%Y Cf. A007088, A030302, A132597, A132575.

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, Aug 24 2007