Finding Sequence Numbers for Fibonacci and Pentanacci Sequences

9/18/2015

Finding the Sequence Number for the Fibonacci Sequence 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. 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 Which equals 999998999999.  This is a sequence number that produces the Fibonacci Sequence in six digit strings.

Finding the Sequence Number for the Pentanacci Numbers (A001591) 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. 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.

David