## Saturday, December 13, 2014

### One of Peggy Sue's Other Numbers

Remember that sweet Italian girl I told you about a month ago.  She's back.  It seems that the coolness of the Tyrrhenian Sea and the heat of Vesuvius creates a temperature difference powerful enough to drive a person's mind into new territories.

The last time we saw a fraction whose decimal expansion produced the 13 times table.  Now we have a fraction whose decimal expansion produces powers of 13.

Powers of 13 beginning with 13^0 through 13^20, in 24 digit chunks:

1 / 999,999,999,999,999,999,999,987 =

0.
000000000000000000000001
000000000000000000000013
000000000000000000000169
000000000000000000002197
000000000000000000028561
000000000000000000371293
000000000000000004826809
000000000000000062748517
000000000000000815730721
000000000000010604499373
000000000000137858491849
000000000001792160394037
000000000023298085122481
000000000302875106592253
000000003937376385699289
000000051185893014090757
000000665416609183179841
000008650415919381337933
000112455406951957393129
001461920290375446110677
019004963774880799438801…

David