Monday, October 12, 2015

Three New Sequence

10/12/2015




Fibonacci Bisection, OEIS sequence A001906
Every Other Fibonacci Numbers (the even numbered terms)
The Sequence Number is 999,997,000,001.
1/999997000001 =
0.
000000  000001  000003  000008  000021  000055  000144  000377  000987  002584  006765  017711  046368  121393 


Bisection of Lucas sequence: Every Other Lucas Number or Just the Odd Indexed Lucas Numbers.
The Sequence Number is:
999,999,960,000,000,499,999,995,000,000,049,999,999,500, 000,004,999,999,950,000,000,499,999,995,000,000,049,999, 999,500,000,004,999,999,950,000,000,499,999,995,000,000, 049,999,999,500,000,006
1/999999960000000499999995000000049999999500000004 99999995000000049999999500000004999999950000000499 9999950000000499999995000000049999999500000006 =
0.
00000000  00000000  00000000  00000000  00000000  00000000  00000000  00000000  00000000  00000000  00000001  00000004  00000011  00000029  00000076  00000199  00000521  00001364  00003571  00009349  00024476  00064079  00167761  00439204  01149851  03010349  07881196  20633239  54018521  
Terms are written in 8 digit strings.
Terms are accurate to the 19th non-zero term.
Compare with OEIS sequence A002878.


The Fibonacci / Lucas sequence.  Terms alternate the even indexed terms are Fibonacci terms, and the odd indexed terms are Lucas terms, beginning with a(0) = 0 which is a Fibonacci term.
(This is a 27-nacci sequence whose non-zero terms are in the OEIS sequence A005013.)
The Sequence Number is:
999,998,999,997,000,003,999,999,999,996,000,003,999,999, 999,996,000,003,999,999,999,996,000,003,999,999,999,996, 000,003,999,999,999,996,000,003,999,999,999,996,000,003, 999,999,999,996,000,003,999,999,999,996,000,005
1/999998999997000003999999999996000003999999999996 00000399999999999600000399999999999600000399999999 99960000039999999999960000039999999999960000039999 99999996000005 =
0.
000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000001  000001  000004  000003  000011  000008  000029  000021  000076  000055  000199  000144  000521  000377  001364  000987  003571  002584  009349  006765  024476  017711  064079  046368  167761  121393  439204  317811 
Terms are written in six digit strings.
Terms are accurate up to the 27th non-zero term.
Compare with OEIS sequence A005013.



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