A211890 Triangle read by rows, where row n starts with n-th prime, followed by n primes in arithmetic progression; T(0,0) = 1 by convention.

1, 2, 3, 3, 5, 7, 5, 11, 17, 23, 7, 37, 67, 97, 127, 11, 71, 131, 191, 251, 311, 13, 244243, 488473, 732703, 976933, 1221163, 1465393, 17, 6947, 13877, 20807, 27737, 34667, 41597, 48527, 19, 546859, 1093699, 1640539, 2187379, 2734219, 3281059, 3827899

Offset

0,2

Comments

T(n,0) = A000040(n) and T(n,k+1) - T(n,k) = A211889(n), 0 <= k < n.

Links

Chai Wah Wu, Rows n=0..10 of triangle, flattened (rows n = 0..9 from Reinhard Zumkeller)

Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.

Wikipedia, Primes in arithmetic progression.

Index entries for sequences related to primes in arithmetic progressions

Example

First 9 rows of triangle:
0:  1
1:  2 3
2:  3 5 7
3:  5 11 17 23
4:  7 37 67 97 127
5:  11 71 131 191 251 311
6:  13 244243 488473 732703 976933 1221163 1465393
7:  17 6947 13877 20807 27737 34667 41597 48527
8:  19 546859 1093699 1640539 2187379 2734219 3281059 3827899 4374739

Prog

(Haskell)
a211890 n k = a211890_tabl !! n !! k
a211890_row n = a211890_tabl !! n
a211890_tabl = zipWith3 (\p k row -> map ((+ p) . (* k)) row)
                        a008578_list (0 : a211889_list) a002262_tabl

Crossrefs

Cf. A007528, A007652, A132231, A214360, A008578, A002262.

Sequence in context: A113460 A113470 A086786 * A231406 A214034 A343224

Adjacent sequences: A211887 A211888 A211889 * A211891 A211892 A211893

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jul 13 2012

Status

approved