Sunday, September 20, 2015

Every Other Fibonacci Number Sequence

9/20/2015



Here is an interesting sequence I ran across.  I was trying new numbers to see if I could find something new.  When I typed the first few terms into OEIS it brought me to this sequence.

Every Other Fibonacci Number (F(2*n)): a(0) = 0, a(1) = 1, and when n>1 then a(n) =3 * a(n-1) - a(n-2).
This produces a list of the odd numbered terms in the Fibonacci Sequence.  (I working on, but have not found a way to do the even numbered terms)
999,997,000,001.
1/999997000001 =
0.
000000  000001  000003  000008  000021  000055  000144  000377  000987  002584  006765  017711  046368  121393  317811 
Written in six digit strings.
Accurate to the 14th non-zero term.
Compare OEIS sequence A001906.



David

2 comments:

  1. 1/999999999997000000000001 =

    0 . 000000000000 000000000001 000000000003 000000000008 000000000021 000000000055 000000000144 000000000377 000000000987 000000002584 000000006765 000000017711 000000046368 000000121393 000000317811 000000832040 000002178309 000005702887 000014930352 000039088169 000102334155 000267914296 000701408733 001836311903 004807526976 012586269025 032951280099 086267571272 225851433717 ...

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