

A106043


First digit other than 9 in the fractional part of the decimal expansion of (1/1000^n)^(1/1000^n).


0



0, 3, 8, 7, 7, 6, 5, 5, 4, 3, 3, 2, 1, 1, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
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OFFSET

0,2


COMMENTS

Even if each term of this sequence were incremented by 1 (to give them a minimum of 1 and a maximum of 9), their distribution would not follow Benford's law (nor does the related sequence whose nth term is the first nonzero digit in the fractional part of the decimal expansion of 1  (1/1000^n)^(1/1000^n)).
For n > 1, a(n)  a(n1) = 0 or 1 except when a(n) = 8 and a(n1) != 8; this situation occurs at n = 2, 15, 145, 1448, ..., and from each such value of n until the next, all non9 digits occur with very nearly equal frequency. E.g., the digits 0..8 occur with frequencies
[ 1, 0, 0, 1, 0, 0, 0, 0, 0] in a(0)..a(1),
[ 1, 2, 1, 2, 1, 2, 1, 2, 1] in a(2)..a(14),
[ 14, 15, 14, 15, 14, 15, 14, 15, 14] in a(15)..a(144),
[145,144,145,145,145,144,145,145,145] in a(145)..a(1447).
(End)


LINKS



EXAMPLE

In each of the decimal expansions in the table below, each 9 has been replaced by an underscore character (to make it easy to see at a glance the first non9 digit in the fractional part):
.
decimal expansion of (1/1000^n)^(1/1000^n)
n with each 9 replaced by "_" a(n)
  
0 1.00000000000000000000000000000000000000000000... 0
1 0.__3116048420_337715764260768851547466351_162... 3
2 0.____8618458487576222544_06332_28167145404344... 8
3 0._______7_276734377780460834_3251023824_06354... 7
4 0.__________72368_78884453188455735031275_4061... 7
5 0._____________6546122360508__11203267556__264... 6
6 0.________________5855346832610717854658364771... 5
7 0.___________________516457130471250406367_124... 5
8 0.______________________44737_57768142_0358356... 4
9 0._________________________3783020248_16076653... 3
10 0.____________________________30_2244721017862... 3
11 0._______________________________240146_1_311_... 2
12 0.__________________________________17106_3665... 1
13 0._____________________________________101__18... 1
14 0.________________________________________032_... 0
15 0.__________________________________________8_... 8
(End)


PROG

(PARI) zerotozero(n) = { local(x, y, z, v, j); for(x=0, n, y=1000^x; v=(1./y)^(1/y); z=Vec(Str(v)); for(j=3, n, if(z[j]<>"9", print1(z[j]", "); break) ) ) }


CROSSREFS



KEYWORD

base,nonn


AUTHOR



STATUS

approved



