A123031 - OEIS

%I #7 Mar 14 2015 00:38:32

%S 2,3,3,5,4,5,7,6,6,7,9,8,7,8,11,11,10,9,9,12,13,13,12,11,10,13,14,17,

%T 15,14,13,12,12,15,18,19,17,16,15,14,13,14,19,20,23,19,18,17,16,15,15,

%U 16,21,24,29,21,20,19,18,17,16,17,20,25,30,31,23,22,21,20,19,18,18,21,22

%N Array read by antidiagonals: row i (i>=0) contains those positive integers n >= 2 for which the multiset { n mod k : k=2,3,...,n } contains exactly one copy of i.

%C In other words, for i >= 1, the i-th row contains all numbers n>2i such that n-i does not have divisors d with i < d < n-i. If p is the smallest prime divisor of n-i then (n-i)/p <= i.

%C Alternatively, the i-th row (i>=1) consists of 2i+1 and positive integers n>2i+1 such that the smallest prime divisor of n-i is greater than or equal to (n-i)/i = n/i - 1.

%e For example, the 0th row obviously contains all prime numbers.

%e The first few rows of the array are

%e 0) 2, 3, 5, 7, 11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,

%e 1) 3, 4, 6, 8, 12,14,18,20,24,30,32,38,42,44,48,54,60,62,68,72,74,80,84,90,98,

%e 2) 5, 6, 7, 9, 13,15,19,21,25,31,33,39,43,45,49,55,61,63,69,73,75,81,85,91,99,

%e 3) 7, 8, 9, 10,12,14,16,20,22,26,32,34,40,44,46,50,56,62,64,70,74,76,82,86,92,

%e 4) 9, 10,11,12,13,15,17,21,23,27,33,35,41,45,47,51,57,63,65,71,75,77,83,87,93,

%e 5) 11,12,13,14,15,16,18,20,22,24,28,30,34,36,42,46,48,52,58,64,66,72,76,78,84,

%e 6) 13,14,15,16,17,18,19,21,23,25,29,31,35,37,43,47,49,53,59,65,67,73,77,79,85,

%e ...

%Y Rows: A000040, A008864, ...; columns: A004280, A051755, ...; diagonal starting with 2: A033627.

%K nonn,tabl

%O 1,1

%A Jared B. Ricks (jaredricks(AT)yahoo.com), Sep 24 2006

%E Additional comments from _Max Alekseyev_, Sep 26 2006