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A182160 Number of iterations of the map n -> sum of the n-powers of the decimal digits of n. 0
0, 8, 3, 25, 18, 57, 8, 169, 181, 1, 61, 164, 177, 573, 209, 785, 288, 1121, 347, 517, 549, 2219, 53, 481, 871, 3144, 878, 3336, 777, 2369, 996, 1577, 655, 5109, 936, 3040, 5290, 1698, 652, 1349, 4000, 2781, 4083, 5559, 2769, 7834, 7098, 4686, 3451, 14278, 5998 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the number of times you form the sum of the n-power of each digit of n before reaching the last number of the cycle.

Generalization and conjecture:

Let a number k. The number of iterations of the orbit k -> sum of the n - power of the decimal digits of k is finite for any exponent n and any starting value k.

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

a(7) = 8 because:

7^7 = 823543;

8^7+2^7+3^7+5^7+4^7+3^7 = 2196163;

2^7+1^7+9^7+6^7+1^7+6^7+3^7 = 5345158;

5^7+3^7+4^7+5^7+1^7+5^7+8^7 = 2350099;

2^7+3^7+5^7+0^7+0^7+9^7+9^7 =  9646378;

9^7+6^7+4^7+6^7+3^7+7^7+8^7 = 8282107;

8^7+2^7+8^7+2^7+1^7+0^7+7^7 = 5018104;

5^7+0^7+1^7+8^7+1^7+0^7+4^7 = 2191663 is the end of the cycle with 8 iterations because 2191663-> 2^7+1^7+9^7+1^7+6^7+6^7+3^7 = 5345158 is already in the trajectory.

MAPLE

with(numtheory) : T :=array(1..20000) :W:=array(1..20000):for n from 1 to 85 do : k:=0:nn:=n:for it from 1 to 20000  do:T :=convert(nn, base, 10) :l:=nops(T):s:=sum(T[i]^n, i=1..l):k:=k+1:W[k]:=s:nn:=s:od: z:= [seq(W[i], i=1..k)]:V:=convert(z, set):n1:=nops(V): printf ( "%d %d \n", n, n1):od:

CROSSREFS

Cf. A182111,  A152077, A160862.

Sequence in context: A065530 A137481 A228886 * A213838 A248294 A004734

Adjacent sequences:  A182157 A182158 A182159 * A182161 A182162 A182163

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Apr 15 2012

STATUS

approved

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Last modified November 15 21:17 EST 2019. Contains 329151 sequences. (Running on oeis4.)