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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
From Jon E. Schoenfield, Feb 21 2021: (Start)
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 n-th 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(n-1) = 0 or -1 except when a(n) = 8 and a(n-1) != 8; this situation occurs at n = 2, 15, 145, 1448, ..., and from each such value of n until the next, all non-9 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
From Jon E. Schoenfield, Feb 21 2021: (Start)
In each of the decimal expansions in the table below, each 9 has been replaced by an underscore character (to make it easy to see at a glance the first non-9 digit in the fractional part):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
Sequence in context: A276120 A197842 A153020 * A294833 A202478 A193720
KEYWORD
base,nonn
AUTHOR
Cino Hilliard, May 06 2005
STATUS
approved

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Last modified February 25 00:32 EST 2024. Contains 370308 sequences. (Running on oeis4.)