[seqfan] Sequences with the first N gcd
Claudio Meller
claudiomeller at gmail.com
Sat Nov 8 13:53:22 CET 2014
Hi seqfans, I´m thinking in two new sequences
a) Find an arrangement of N+1 integers in a row such that the gcd of
every two contiguous integers produce the first N integers from 1 to
N, not necesarily in order but such that the sum of the N+1 integers
is a minimal sum.
Example:
N=1 Numbers 1 1 Sum = 2
gcd 1
N=2 Numbers 1 2 2 Sum=5
gcd 1 2
N=3 Numbers 2 2 3 3 Sum=10
gcd 2 1 3
N=4 Numbers 4 4 2 3 3 Sum=16
gcd 4 2 1 3
N=5 Numbers 5 5 4 4 6 3 Sum =27
gcd 5 1 4 2 3
N=6 Numbers 5 5 4 4 6 6 3 Sum=33
-- gcd 5 1 4 2 6 3
So if there is not a mistake in my calculations 2, 5, 10, 16, 27, 33
b) Same as a) but with distinct numbers
N=1 Numbers 1 2 Sum = 3
gcd 1
N=2 Numbers 1 2 4 Sum = 7
gcd 1 2
N=3 Numbers 3 6 2 1 Sum = 12
gcd 3 2 1
So 3, 7, 12, etc
You can see the problems in my blog
http://simplementenumeros.blogspot.com.ar/2014/11/1360-mcd.html
and in Carlos Rivera site:
http://www.primepuzzles.net/puzzles/puzz_764.htm
Claudio Meller
http://grageasdefarmacia.blogspot.com
http://todoanagramas.blogspot.com/
http://simplementenumeros.blogspot.com/
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