login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327263 Array T(n,k) in which the i-th row consists of numbers > 1 not in the array U(i;n,k) = (i*n*k - (i-2)*A319929(n,k))/2 where i >= 1, n >= 1 and k >= 1, read by antidiagonals. 6
3, 5, 2, 9, 3, 2, 13, 5, 3, 2, 21, 7, 4, 3, 2, 25, 11, 5, 4, 3, 2, 33, 13, 7, 5, 4, 3, 2, 37, 17, 9, 6, 5, 4, 3, 2, 45, 19, 10, 7, 6, 5, 4, 3, 2, 57, 23, 13, 9, 7, 6, 5, 4, 3, 2, 61, 29, 15, 11, 8, 7, 6, 5, 4, 3, 2, 73, 31, 17, 12, 9, 8, 7, 6, 5, 4, 3, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All the U(i;n,k) mimic the ordinary multiplication table in that they are commutative, associative, have identity element 1 and have 0. However (except when i=2) they are partially distributive, meaning that distributivity works except if an even number is partitioned into a sum of two odd numbers. Only when i=2, the odd-even-dependent A319929 term disappears and normal distributivity holds.

U(0;n,k) = A319929(n,k);

U(1;n,k) = A322630(n,k);

U(2;n,k) = n*k;

U(3;n,k) = A322744(n,k);

U(4;n,k) = A327259(n,k);

U(i;n,k) = 2i*floor(n/2)*floor(k/2) + A319929(n,k).

Row 1 is 2p-1 where p is a prime number (A076274 without 1).

Row 2 is the prime numbers.

Row 3 is A307002 without 1.

Row 4 is A327261 without 1.

The i-th row of T(n,k) consists of numbers that sieve out of the array U(i;n,k) = (i*n*k - (i-2)*A319929(n,k))/2, in numerical order.

LINKS

Table of n, a(n) for n=1..78.

FORMULA

With one exception there are likely no formulas for the rows of T(n,k) since their creation is based on a sieving process like the familiar prime number sieve. The exception is T(1,k) = 2*T(2,k)-1.

EXAMPLE

3  5  9  13  21  25  33  37  45  57  61  73  81  85  93 105 117 121 133 141 145 ...

2  3  5   7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73 ...

2  3  4   5   7   9  10  13  15  17  21  22  23  25  29  31  34  37  39  41  45 ...

2  3  4   5   6   7   9  11  12  14  15  17  19  21  22  25  27  28  29  31  35 ...

2  3  4   5   6   7   8   9  11  13  14  16  17  18  19  21  23  25  26  28  29 ...

2  3  4   5   6   7   8   9  10  11  13  15  16  18  19  20  21  22  23  25  27 ...

2  3  4   5   6   7   8   9  10  11  12  13  15  16  17  18  20  21  22  23  24 ...

2  3  4   5   6   7   8   9  10  11  12  13  14  15  17  19  20  22  23  24  25 ...

2  3  4   5   6   7   8   9  10  11  12  13  14  15  16  17  19  21  22  24  25 ...

2  3  4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  21  23  24 ...

...

CROSSREFS

Cf. A000040, A003991, A076274, A319929, A322630, A322744, A327259.

Sequence in context: A026143 A075626 A152649 * A186412 A322982 A275846

Adjacent sequences:  A327260 A327261 A327262 * A327264 A327265 A327266

KEYWORD

nonn,tabl

AUTHOR

David Lovler, Oct 15 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 13 04:31 EDT 2020. Contains 335673 sequences. (Running on oeis4.)