Verification of the periodic nature of the final digit in A006003
Andrew Plewe
aplewe at sbcglobal.net
Sun Sep 12 02:28:58 CEST 2004
While musing generally on the connections between Magic Squares and
prime numbers, I noticed that the sequence of the final digit of each
member of the Magic Square constant sequence (A066886) is periodic. At
least it seems to be, with a period of 20. I'd like to submit this to
the OEIS, but I'd like to confirm if it is indeed periodic first. The
sequence (starting with n = 0 thru n = 19):
0, 1, 5, 5, 4, 5, 1, 5, 0, 9, 5, 1, 0, 5, 9, 5, 6, 5, 5, 9
Note: Perhaps there ought to be a link to A006003 provided in the
entry for A066886, which has an interesting discussion of the
distribution of primes for some prime p in a p by p array, filled from
top to bottom with the integers from 1 to p^2. While this does not
produce a magic square, the sums of the diagonals and the median
horizontal and vertical rows equal the magic constant as calculated for
p.
-Andrew Plewe-
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