Sequence
Number that show Powers of a Number:
“1,000,000 – n” will produce a sequence
number that shows “the powers of n”, beginning with n^{0}, n^{1},
n^{2}, etc., written in 6 digit strings.
“1,000,000,000,000 – n” will produce a
Sequence Number that produces a list of the powers of n, beginning with n^{0},
n^{1}, n^{2}, etc., written in 12 digit strings.
Examples:
Powers of 3:
1,000,000 – 3 = 999,997. So the Sequence Number is 999,997
1/999997 =
0.
000001 000003 000009 000027 000081 000243 000729 002187 006561 019683 059049 177147 …
This Sequence number produce a list of
the powers of three, written in 6 digit strings, from 3^{0} through 3^{11}
(12 nonzero terms).

Powers of 23:
1,000,000 – 23 = 999,977. So the Sequence Number is 999,977.
1/999977 =
0.
000001 000023 000529 012167 …
This Sequence Number produces a list of
the powers of 23, written in six digit strings, from 23^{0} to 23^{3}. Since this only produces 4 terms, we would
want to rewrite the Sequence number so that more terms could be shown.
1,000,000,000 – 23 = 999,999,977. So our new Sequence number is 999,999,977
1/999999977 =
0.
000000001 000000023 000000529 000012167 000279841 006436343
Written in nine digit strings.
This sequence now shows 6 valid and
accurate terms, and 999,999,977 is considered a valid Sequence Number.
Compare with OEIS sequence A009967.

“1,000,000,000,000 – n” will produce a
sequence of “the powers of n”, beginning with n^{0}, n^{1}, n^{2},
etc., written in 12 digit strings.
Example:
1,000,000,000,000 – 95 =
999,999,999,905.
Powers of 95
999,999,999,905
1/999999999905 =
0.
000000000001 000000000095 000000009025 000000857375 000081450625 007737809375 …
Written in 12 digit strings.
Accurate to the sixth nonzero term.

“1,000,000,000,000,000,000 – n” will
produce a sequence of “the powers of n”, beginning with n^{0}, n^{1},
n^{2}, etc., written in 18 digit strings.
Example:
1,000,000,000,000,000,000 – 123 =
999,999,999,999,999,877.
Powers of 123
The sequence number that produces powers
of 123 in 18 digit strings is 999,999,999,999,999,877
1/999999999999999877 =
0.
000000000000000001 000000000000000123 000000000000015129 000000000001860867 000000000228886641 000000028153056843 000003462825991689 000425927596977747 …
Written in 18 digit strings.
Accurate to the eighth nonzero term.

We are able to continue using this pattern
to expand the sequence to show whatever size digit strings are needed or to
lengthen the number of terms which are accurate.
David
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