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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. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 k iterations (k >= 0) we reach the following sequences:

0th step: A001477: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, ...

1st step: A175420: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 0, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 0, ...

2nd step: A175421: 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, 25, 216, 6561, 4096, 1, 0, 1, 8, 49, 4096, 25, 36, 531441, 32, 22876792454961 0, 1, 6, 1, 60466176, 244140625, 101559956668416 1, 1, 1, 0, ...

3rd step: A175422: 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, 25, 36, 1, 1, 1, 0, 1, 8, 6561, 1, 25, 216, 1, 8, 1, 0, 1, 6, 1, 1, 1, 1, 1, 1, 1, 0, ...

4th step: A175423: 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, 25, 216, 1, 1, 1, 0, 1, 8, 1, 1, 25, 36, 1, 8, 1, 0, 1, 6, 1, 1, 1, 1, 1, 1, 1, 0, ...

LINKS

Table of n, a(n) for n=0..100.

EXAMPLE

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 - A175427.

Sequence in context: A217657 A010879 A179636 * A175422 A175423 A175421

Adjacent sequences:  A175416 A175417 A175418 * A175420 A175421 A175422

KEYWORD

sign,base

AUTHOR

Jaroslav Krizek, May 09 2010

STATUS

approved

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Last modified May 23 08:43 EDT 2017. Contains 286909 sequences.