A175419 The single-digit number obtained by iterated mapping of r (starting with n) to a power-tower of its digits, or -1 if such a single-digit number is never reached.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 4, 9, 6, -1, -1, 1, 1, 1, 0, 1, 8, 1, 1, -1, -1, 1, 8, 1, 0, 1, 6, 1, 1, 1, 1, 1, 1, 1, 0, 1, 8, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Jaroslav Krizek, May 09 2010

Keywords

• sign
• base

Comments

Define a map r->A175420(r) which takes the base-10 digits of r = Sum_{i>=0} d_i*10^i and assigns the power-tower ((d_0^d_1)^d_2)^d^3... to the result. There are A055642(r)-1 exponentiations in this expression. Single-digit numbers are fixed points of the map.

Starting with n, this map is iterated as often as needed to result in a single-digit number, which becomes a(n). In case the iteration does not reach a single-digit number (i.e., enters cycles with only multi-digit numbers), a(n)= -1.

The entries 1 to 9 appear infinitely often in the sequence.

The entry -1 appears infinitely often in the sequence, see A175426.

After 1 to 4 iterations we reach sequences A175420 to A175423.

Examples

			For n = 33: a(33) = 1 because starting with 33 we reach a single-digit 1 after 4 iterations: 3^3 = 27, 7^2 = 49, 9^4 = 6561, ((1^6)^5)^6 = 1.
For n = 25: a(25) = -1 because starting with 25 the iteration enters a loop of 2-digit numbers: 5^2 = 25, 5^2 = 25, ...
		

Crossrefs

Cf. A175420, A175421, A175422, A175423, A175424, A175425, A175426, A175427.