Wednesday, October 21, 2015

Every Number has a Story to Tell

10/31/2015

Every Number has a Story to Tell:
Todays Story as told by
999,999,899,999,989,999,998,999,999,899,999,989,999,
998,999,999,899,999,989,999,998,999,999,899,999,989,
999,998,999,999,899,999,989,999,998,999,999,899,999,
989,999,998,999,999,899,999,989,999,998,999,999,899,
999,989,999,998,999,999,899,999,989,999,999
With 189 digits, few mathematicians have studied this number.
It’s an odd number.
It’s also a composite number.  Its prime factors are: 7 × 17 × 22646166595363  × 371072095968871744838913138769681036025474172553597749182624587489701884731836964006159703359380791727133473366600646185929079002940864276860121574110696897424044571076436467
Those are the easy properties to find.  But what is amazing is what happens when you take its inverse:
The 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 “27-nacci” Sequence (or just “27-nacci” Sequence):
Defined as: a(0) = … = a(25) = 0, a(26) = 1, and when n>26 then a(n) = a(n-1) + a(2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) + a(n-8) + a(n-9) + a(n-10) + a(11) + a(12) + a(n-13) + a(n-14) + a(n-15) + a(n-16) + a(n-17) + a(n-18) + a(n-19) + a(20) + a(n-21) + a(n-22) + a(n-23) + a(n-24) + a(n-25) + a(n-26) + a(n-27).
The Sequence Number is"
999,999,899,999,989,999,998,999,999,899,999,989,999,
998,999,999,899,999,989,999,998,999,999,899,999,989,
999,998,999,999,899,999,989,999,998,999,999,899,999,
989,999,998,999,999,899,999,989,999,998,999,999,899,
999,989,999,998,999,999,899,999,989,999,999
Its inverse is:
1/999999899999989999998999999899999989999998999
99989999998999999899999989999998999999899999989
99999899999989999998999999899999989999998999999
89999998999999899999989999998999999899999989999
999
And it's decimal expansion is:
0.
0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000000  0000001  0000001  0000002  0000004  0000008  0000016  0000032  0000064  0000128  0000256  0000512  0001024  0002048  0004096  0008192  0016384  0032768  0065536  0131072  0262144  0524288  1048576  2097152  4194304
Terms are written in seven digit strings.
Terms are accurate up to the 24th non-zero term, the 2nd to the last seven digit term in this sequence.
This sequence is not found in the OEIS collection.  You will only find it here or at the Sequence Number blog.
Don't be afraid of the BIG NUMBERS.  That's where the good stuff starts happening.

David