A096370 a(n) is one greater than the number of repeated applications of the Reverse and Add (RA) transform applied to the binary representation of n that are required to reach a palindrome, or a(n)=0 if a palindrome is never reached.

1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 5, 6, 1, 0, 3, 2, 5, 0, 1, 0, 3, 2, 1, 2, 1, 2, 0, 2, 0, 2, 3, 2, 0, 2, 3, 4, 1, 0, 0, 2, 0, 4, 1, 2, 3, 4, 3, 2, 3, 4, 3, 0, 0, 2, 1, 2, 1, 2, 0, 2, 3, 2, 5, 4, 1, 12, 0, 6, 0, 0, 3, 2, 3, 2, 5, 0, 1, 0, 3, 6, 0, 0, 3, 4, 1, 0, 0, 2, 0, 4, 1, 2, 5, 2, 11, 12

Offset

1,2

Links

Table of n, a(n) for n=1..104.

Example

For n=20, we have 20=10100 (base 2) and
(RA^0)10100=10100
(RA^1)10100=11001
(RA^2)10100=101100
(RA^3)10100=111001
(RA^4)10100=1100000
(RA^5)10100=1100011 (a palindrome).
Thus a(20)=5+1=6.
For n=22, we get
(RA^9)=> 1101000101
(RA^13)=> 110010001101
(RA^17)=> 11000100011101
(RA^21)=> 1100001000111101
(RA^25)=>110000010001111101
(RA^(4k+1)=>1^2 0^(k-1) 1 0^3 1^(k-1) 0 1, where here 0^k denotes 000...0 (k times). A regular pattern also occurs for the intermediate values, showing that a palindrome never occurs. Thus a(22)=0.

Crossrefs

Sequence in context: A354599 A303536 A259656 * A330721 A076622 A194513

Adjacent sequences: A096367 A096368 A096369 * A096371 A096372 A096373

Keyword

nonn,base

Author

John W. Layman, Jul 19 2004

Status

approved