A132601 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.

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

Offset

1,2

Comments

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

A132603 and A132604 give record values and where they occur;

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

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

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Example

S(0) = 110111001011101111000100110101011 ..;
for n<=2: a(n)=n, S(n) = S(n-1);
n=3->'11', a(3)=1->'1', S(3)=10111001011101111000100110101011..;
n=4->'100', a(4)=5->'101', S(4)=10111011011101111000100110101011..;
n=5->'101', a(5)=1->'1', S(5)=111011011101111000100110101011..;
n=6->'110', a(6)=2->'10', S(6)=11011011101111000100110101011..;
n=7->'111', a(7)=7->'111', S(7)=S(6);
n=8->'1000', a(8)=14->'1110', S(8)=11011011101111110100110101011..;
n=9->'1001', a(9)=18->'10010', S(9)=110110111011111101001010101011..;
n=10->'1010', a(10)=16->'10000',
S(10)=1101101110111111000001010101011..;
n=11->'1011', a(11)=2->'10', S(11)=11001110111111000001010101011..;
n=12->'1100', a(12)=1->'1', S(12)=11110111111000001010101011..;
n=13->'1101', a(13)=3->'11', S(13)=111111111000001010101011..;
n=14->'1110', a(14)=7->'111', S(14)=11111111000001010101011..;
n=15->'1111', a(15)=1->'1', S(15)=111111000001010101011..;
n=16->'10000', a(16)=6->'110', S(16)=1111111001010101011.. .

Crossrefs

Cf. A007088, A030302, A132597, A132575.

Sequence in context: A353577 A200778 A345355 * A047818 A055972 A342414

Adjacent sequences: A132598 A132599 A132600 * A132602 A132603 A132604

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 24 2007

Status

approved