[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/