A083825 a(1) = 12; then numbers obtained at every stage of division by 9 in the following process. multiply by 9, reverse the digits, divide by 9, reverse the digits, multiply by 9, reverse the digit, divide by 9, ...

12, 89, 32, 78, 43, 67, 54, 56, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 09 2003

Keywords

• base
• easy
• nonn

Comments

The interesting pattern of terminating at 65 after which every term is 65 is visible. 89 onwards alternate terms are obtained by subtracting 11 and 32 onwards alternate terms are obtained by adding 11 and both terminate at 65. Conjecture: Every such sequence for an n-digit number not divisible by 10 terminates in another n-digit number. Let it be t(n), then one also gets t(10k) =t(k). E.g. t(12) = 65. Subsidiary sequence:(1) a(n) = t(n), a(10k) = a(k). (2). The index of the first occurrence of t(n). A measure of the length of the cycle.

Examples

			*12--->108--->801--->*89--->98--->882---288-->*32--->23--->207--->702--->*78--->87--->783--->387--->*43--->34--->306--->603--->*67--->76...
		

Crossrefs

Cf. A083822, A083823, A083824.