A175403 a(n) is the smallest number m requiring n iterations {((((D_1^D_2)^D_3)^D_4)^...)^D_k to reach a one-digit number starting at r = n, where D_k is the k-th digit D of the number r and k is the digit number of the number r in the decimal expansion of r (A055642)}.

0, 10, 24, 26, 29

Offset: 0

Author

Jaroslav Krizek, May 01 2010

Keywords

• nonn
• base
• more

Comments

Conjecture: sequence is finite.

Assuming that A020665(2) = 86, A020665(3) = 68, A020665(5) = 58 and A020665(7) = 35, a(4) is the last term; see A175402.

Examples

			For n = 4: a(4) = 29 because 29 is the smallest number with 4 steps of defined iteration: {2^9 = 512}, {(5^1)^2 = 25}, {2^5 = 32}, {3^2 = 9}.
		

Crossrefs

Cf. A020665, A175398, A175399, A175400, A175401, A175402, A175405.

Extensions

Comment and edits from Charles R Greathouse IV, Aug 03 2010

Further edits from N. J. A. Sloane, Aug 08 2010. I am still worried that n is mentioned too many times in the definition.