[seqfan] plastic number base

Dale Gerdemann dale.gerdemann at gmail.com
Tue Jul 9 10:31:22 CEST 2013


Hello Seqfans,


Suppose we represent numbers in "plastic number base" (like golden ratio
base  but using the plastic number instead of the golden ratio). There are
some numbers that are expressed using a surprisingly small number of terms.
For example, 10717 requires the following powers of the plastic number:
[33, -18, -42, -47, -53, -67]. Here's  a  small list of examplesL:


10717  [33, -18, -42, -47, -53, -67]
12214  [33, 26, -11, -19, -29, -42, -67]
14197  [34, -19, -24, -33, -42, -47, -54, -67]
24914  [36, -16, -24, -33, -39, -47, -65, -72]
57918  [39, -19, -26, -31, -37, -49, -54, -60, -68, -74, -80]
101639 [41, -19, -28, -34, -51, -64, -72, -80]
115836 [41, 34, -16, -31, -41, -54, -63, -70, -76, -85]
192561 [43, 34, -20, -27, -42, -48, -58, -67, -75, -85]
236282 [44, -20, -33, -42, -51, -57, -62, -80, -85]
370925 [45, 39, -22, -32, -42, -50, -59, -73, -79, -87, -93]
414646 [46, -23, -30, -42, -57, -74, -87, -93]

Is there any signicance to these numbers?



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