999,998 is a Sequence Number that will
generate a list of the powers of 2 (2^0, 2^1, 2^2, 2^3, 2^4, etc.), written
in six digit strings.
The inverse of this number is:
1/999998 =
The decimal expansion of this number is:
(I have separated the terms with spaces
to make it easier to read.)
0.
000001 000002 000004 000008 000016 000032 000064 000128 000256 000512 001024 002048 004096 008192 016384 032768 065536 131072 262144 …
The sequence above accurately shows the
first 19 terms. If we want a longer
sequence, we will need to use a larger sequence number. I will show you how to do that later.
If you would like to check the accuracy
of these terms you can compare it with the Online Encyclopedia of Integer
Sequences: http://oeis.org/A000079 and http://oeis.org/A000079/b000079.txt.
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Let’s try something more
difficult.
999,999,999,993 is a
Sequence Number that generates a list of the powers of 7 (7^0, 7^1, 7^2, 7^3,
7^4, etc.), with terms written in 12 digit strings.
The inverse of this
sequence number:
1/999999999993 =
The decimal expansion of
this fraction is:
0.
000000000001 000000000007 000000000049 000000000343 000000002401 000000016807 000000117649 000000823543 000005764801 000040353607 000282475249 001977326743 013841287201 096889010407 ...
The first 12 terms of
this sequence are accurately shown above.
If you want to check the
accuracy of these terms you can check the Online Encyclopedia of Integer
Sequences: http://oeis.org/A000420 and http://oeis.org/A000420/b000420.txt.
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But these are two
easy. Let’s try to get up to date and
produce a list of the powers of 2016.
999,999,999,999,999,999,997,984
is a Sequence Number that will generate a list of the powers of 2016 (2016^0,
2016^1, 2016^2, 2016^3, 2016^4, etc.), with terms written in 24 digit
strings.
The inverse of this
Sequence Number is:
1/999999999999999999997984
=
The decimal expansion of
this fraction is:
0.
000000000000000000000001 000000000000000000002016 000000000000000004064256 000000000000008193540096 000000000016518176833536 000000033300644496408576 000067134099304759689216 ...
The first seven terms in
this sequence are accurately shown above.
The Online Encyclopedia of
Integer Sequence does not contain this sequence in their collection.
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The powers of 5 (5^0, 5^1,
5^2, 5^3, 5^4, etc.)
A Sequence Number that
will generate a list of the powers of 5, written in 19 digit strings is:
9,999,999,999,999,999,995
The inverse of this
number is:
1/9999999999999999995 =
And the decimal
expansion of this fraction is:
0.
0000000000000000001 0000000000000000005 0000000000000000025 0000000000000000125 0000000000000000625 0000000000000003125 0000000000000015625 0000000000000078125 0000000000000390625 0000000000001953125 0000000000009765625 0000000000048828125 0000000000244140625 0000000001220703125 0000000006103515625 0000000030517578125 0000000152587890625 0000000762939453125 0000003814697265625 0000019073486328125 0000095367431640625 0000476837158203125 0002384185791015625 0011920928955078125 0059604644775390625 0298023223876953125 1490116119384765625 …
The first 27 terms in
this sequence are accurately shown above.
We got all of the terms up to 18 digits long, and one 19 digit digit
term before this Sequence Number made an error.
If we want more terms
(longer terms) all we have to do is adjust our Sequences Number by adding nines
to the front of our Sequence Number.
You can compare these
results with the Online Encyclopedia of Integer Sequences at: http://oeis.org/A000351 and http://oeis.org/A000351/b000351.txt.
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