## Friday, May 15, 2015

### More NERDY numbers - The Fibonacci Sequence

OK – I’m still having technical problems – let me try something different.

 The Fibonacci Sequence is generated manually by starting with two values: a(0) = 1, and a(1) = 1.  Then we simple add the two previous values to get the next value: when n>1, then a(n) = a(n-1) + a(n-2). The Fibonacci Sequence can be generated by a “Nerdy number”.  This number is 999998999999.  When we calculate the decimal expansion of the reciprocal (or inverse) we get each term in the Fibonacci Sequence, written in 6 digit chunks, until the terms get too large and start overlapping.  I have place spaces in the expansion to help you pick out the individual terms in the sequence: 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 832041 … Another Nerdy number shows the Fibonacci Sequence written in 12 digit chunks: 1/999999999998999999999999 = 0. 000000000000 000000000001 000000000001 000000000002 000000000003 000000000005 000000000008 000000000013 000000000021 000000000034 000000000055 000000000089 000000000144 000000000233 000000000377 000000000610 000000000987 000000001597 000000002584 000000004181 000000006765 000000010946 000000017711 000000028657 000000046368 000000075025 000000121393 000000196418 000000317811 000000514229 000000832040 000001346269 000002178309 000003524578 000005702887 000009227465 000014930352 000024157817 000039088169 000063245986 000102334155 000165580141 000267914296 000433494437 000701408733 001134903170 001836311903 002971215073 004807526976 007778742049 012586269025 020365011074 032951280099 053316291173 086267571272 139583862445 225851433717 365435296162 591286729879 956722026042 … How does a 24 digit number (all 9s except for one 8) know how to spit out the first 60 Fibonacci number?