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A123031 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. 0
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, 15, 14, 13, 12, 12, 15, 18, 19, 17, 16, 15, 14, 13, 14, 19, 20, 23, 19, 18, 17, 16, 15, 15, 16, 21, 24, 29, 21, 20, 19, 18, 17, 16, 17, 20, 25, 30, 31, 23, 22, 21, 20, 19, 18, 18, 21, 22 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

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.

LINKS

Table of n, a(n) for n=1..75.

EXAMPLE

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

The first few rows of the array are

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,

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,

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,

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,

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,

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,

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,

...

CROSSREFS

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

Sequence in context: A273494 A116922 A086898 * A271709 A159070 A088241

Adjacent sequences:  A123028 A123029 A123030 * A123032 A123033 A123034

KEYWORD

nonn,tabl

AUTHOR

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

EXTENSIONS

Additional comments from Max Alekseyev, Sep 26 2006

STATUS

approved

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Last modified August 7 10:19 EDT 2022. Contains 355985 sequences. (Running on oeis4.)