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Question from Vishal, a student:

this is known as rat sequence. I want to know the logic pf this :-

1,2,4,8,16,77,145

Vishal,

See the on-line encyclopedia of integer sequences:
http://www.research.att.com/~njas/sequences/A004000

RATS: Reverse Add Then Sort the digits applied to previous term, starting with 1.
COMMENT
It is conjectured that no matter what the starting term is, repeatedly applying RATS leads either to this sequence or into a cycle of finite length, such as those in A066710 and A066711.

FORMULA
Let a(n) = k, form m by Reversing the digits of k, Add m to k Then Sort the digits of the sum into increasing order to get a(n+1).

EXAMPLE
668 -> 668 + 866 = 1534 -> 1345.

Chris

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