Examples of How to Find Sequence Numbers
Finding the Sequence Number for the
Fibonacci Sequence (OEIS A000045) by working backwards.
First go to the OEIS website, go to the
page for sequence A000045 (www.oeis.org/A00045 ), and copy all of
the terms of the Fibonacci Sequence that are 6 digits or less (the first 30 terms).
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,
89, 144, 233, 377, 610, 987,
1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040
Then add zeros as needed so that each
term has 6 digits,
000000, 000001, 000001, 000002, 000003,
000005, 000008,
000013, 000021, 000034, 000055, 000089, 000144, 000233, 000377, 000610, 000987, 000597, 002584, 004181, 006765, 010946, 017711, 028657, 046368, 075025, 121393, 196418, 317811, 514229, 832040
Next take out the commas and spaces,
put a “0.” in front, and
take the inverse (raise it to the 1 power).
0.0000000000010000010000020000030000050000080000130
000210000340000550000890001440002330003770006100009 870015970025840041810067650109460177110286570463680 75025121393196418317811514229832040^1
Take this over to the Wolfram Alpha
website to do our calculation (www.wolframalpha.com ). Just put the expression above into the blank box at the top of the page and hit “enter”.
The result is:
9.9999899999900000000000000000000000000000000000000
00000... × 10^11
So our sequence number is 999998999999
(I hope) Let’ check it
out at the Wolfram alpha website. 
999,998,999,999
1/999998999999 =
0.
000000 000001 000001 000002 000003 000005 000008 000013 000021 000034 000055 000089 000144 000233 000377 000610 000987 001597 002584 004181 006765 010946 017711 028657 046368 075025 121393 196418 317811 514229 …
The terms are written in 6 digit
strings.
The terms are accurate up to the 29^{th}
nonzero term. The 30^{th}
term has an error because the 31^{st} term is seven digits long and
overlaps the 30^{th} term, changing the 30^{th} term to
832041 – which as I said, is not correct.
This is a sequence number that produces
the Fibonacci Sequence in six digit strings as predicted. If
you would like to see it produce more terms try 999,999,999,998,999,999,999,999
– it will produce terms that are 12 digits long.

Finding the Sequence Number for the
Pentanacci Numbers
(OEIS A001591) by working backwards.
Copy the terms of the Pentanacci
Sequence up through all of
the six digit terms.
0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61,
120, 236, 464, 912, 1793,
3525, 6930, 13624, 26784, 52656, 103519, 203513, 400096, 786568
Add zeros to make every term six
digits, take out the commas
and spaces, add a “0.” on the front, and take the inverse (tac a “^1” on the back end).
0.0000000000000000000000000000010000010000020000040
000080000160000310000610001200002360004640009120017 930035250069300136240267840526561035192035134000967 86568^1
Do the calculation.
9.9999899999899999899999899999900000000000000000000
00000... × 10^29
Which equals: 999998999998999998999998999999. This
sequence number produces the Pentanacci Sequence written in six digit strings. Other sequence numbers related to this one will produce longer string and more terms if needed or desired. 999999999998999999999998999999999998999999999998999 999999999 will produce terms in 12 digit terms, about twice as many terms as the previous number. 
Fibonacci Bisection, (OEIS A001906)
Every Other Fibonacci Numbers (the even
numbered terms)
First 16 terms are:
0, 1, 3, 8, 21, 55, 144, 377, 987,
2584, 6765, 17711, 46368, 121393, 317811, 832040
Turn each term into a six digit string,
take out the commas and
the spaces, put a “0.” in the front and a “^1” in the back. This will give you:
0.000000000001000003000008000021000055000144000
37700098700258400676501771104636812139331781183 2040^1
Plug the above number into Wolfram
Alpha and you will get the following result:
9.999970000010000000000000000000000000000000000
000000000... × 10^11
It looks like the sequence number will
be 999,997,000,001.
So let’s check it out – see if it
works.
1/999997000001 =
0.
000000 000001 000003 000008 000021 000055 000144 000377 000987 002584 006765 017711 046368 121393 317811 …
Terms are written in six digit strings.
Terms are accurate up to the 14^{th}
nonzero term.
Additional terms can be displayed by
showing 12 digit terms using the sequence number: 999,999,999,997,000,000,000,001.

The Other Every Other Fibonacci
Numbers, A001519
OEIS describes this sequence as a
bisection of the Fibonacci Sequence, listing the odd terms – but they include
both 1s in this sequence and one of these must be an even numbered term.
I have not yet been able to find a
Sequence Number that works for this sequence.
I suspect that there is no Sequence number that works for this
sequence, but I am not closing the door on this one. I really would like to find it if one
exists.

This method of finding sequence numbers
can be used on other number sequences also.
However, not all sequences have a sequence number that will produce
them. Very few do. But you won’t know unless you try.
In the past though, I have found that I
can often find sequence numbers for counting sequences, multiplying sequences,
power sequence and Fibonacci like sequences (along with a few miscellaneous sequences).
I am working on a lesson to explain how
the Fibonacci like sequences work. I was
not satisfied with my first draft. I am
working on a rewrite that will break it up into two lessons – and have a surprise
ending.
David
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