Oscarlevin at 21:59, 10 November 2014

2014-11-10T21:59:39Z

← Older revision		Revision as of 15:59, 10 November 2014
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	# Every positive integer is the sum of numbers from the list,		# Every positive integer is the sum of numbers from the list,
	# no number on the list appears more than once in any one sum, and		# no number on the list appears more than once in any one sum, and
	# no two consecutive numbers on the list, that is, <m>a_k</m>, <m>a_{k+1}, appear in any one sum.		# no two consecutive numbers on the list, that is, <m>a_k</m>, <m>a_{k+1}</m>, appear in any one sum.

	(Note that an integer is considered to be the sum of one number on the list if it is actually on the list. Also, for the terminally picky, "fewest possible" refers to inclusion, not to cardinality.)		(Note that an integer is considered to be the sum of one number on the list if it is actually on the list. Also, for the terminally picky, "fewest possible" refers to inclusion, not to cardinality.)

Oscarlevin: Created page with "Find an ordered list of positive integers, a_1, a_2,\ldots with the fewest possible integers, satisfying all the following properties: # Every positive integer is the..."

2014-11-10T21:59:10Z

Created page with "Find an ordered list of positive integers, <m>a_1, a_2,\ldots</m> with the fewest possible integers, satisfying all the following properties: # Every positive integer is the..."

New page

Find an ordered list of positive integers, <m>a_1, a_2,\ldots</m> with the fewest possible integers, satisfying all the following properties:

# Every positive integer is the sum of numbers from the list,
# no number on the list appears more than once in any one sum, and
# no two consecutive numbers on the list, that is, <m>a_k</m>, <m>a_{k+1}, appear in any one sum.

(Note that an integer is considered to be the sum of one number on the list if it is actually on the list. Also, for the terminally picky, "fewest possible" refers to inclusion, not to cardinality.)

In symbols, for any positive integer <m>n</m>

:<m>n = \sum b_i a_i</m>

where the sum runs over all elements of the list, <m>b_i = 0</m> or 1, and <m>b_i b_{i+1} = 0</m>.

{{Bpow}}

Draft:Bpow60 - Revision history

Oscarlevin at 21:59, 10 November 2014

Oscarlevin: Created page with "Find an ordered list of positive integers, a_1, a_2,\ldots with the fewest possible integers, satisfying all the following properties: # Every positive integer is the..."