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A199333 Triangle read by rows: T(n,0) = T(n,n) = 1, 0 < k < n: T(n,k) = smallest prime not less than T(n-1,k) + T(n-1,k-1). 8
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 7, 5, 1, 1, 7, 13, 13, 7, 1, 1, 11, 23, 29, 23, 11, 1, 1, 13, 37, 53, 53, 37, 13, 1, 1, 17, 53, 97, 107, 97, 53, 17, 1, 1, 19, 71, 151, 211, 211, 151, 71, 19, 1, 1, 23, 97, 223, 367, 431, 367, 223, 97, 23, 1, 1, 29, 127 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(n,k) = T(n,n-k);

T(n,0) = 1, cf. A000012;

T(n,1) = A008578(n), n > 0;

A199424(n) = first row in triangle A199302 containing n-th prime;

A199425(n) = number of distinct primes in rows 0 through n;

large terms in the b-file are probable primes only, row number > 50.

LINKS

Reinhard Zumkeller, Rows n=0..150 of triangle, flattened

Index entries for triangles and arrays related to Pascal's triangle

FORMULA

T(n,k) = A007918(T(n-1,k)+T(n-1,k-1), 0 < k < n, T(n,0) = T(n,n) = 1.

EXAMPLE

0:                 1

1:               1   1

2:             1   2   1

3:           1   3   3   1

4:         1   5   7   5   1

5:       1   7  13  13   7   1

6:     1  11  23  29  23  11   1

7:   1  13  37  53  53  37  13   1

8: 1  17  53  97 107  97  53  17   1

primes in 8th row:

T(7,0)+T(7,1) = 1+13 = 14 --> T(8,1) = T(8,7) = 19;

T(7,1)+T(7,2) = 13+37 = 50 --> T(8,2) = T(8,6) = 53, already in row 7;

T(7,2)+T(7,3) = 37+53 = 90 --> T(8,3) = T(8,5) = 97;

T(7,3)+T(7,4) = 53+53 = 106 --> T(8,4) = 107.

PROG

(Haskell)

a199333 n k = a199333_tabl !! n !! k

a199333_row n = a199333_tabl !! n

a199333_list = concat a199333_tabl

a199333_tabl = iterate

   (\row -> map a159477 $ zipWith (+) ([0] ++ row) (row ++ [0])) [1]

CROSSREFS

Cf. A159477; A199581 & A199582 (central terms), A199694 (row sums), A199695 & A199696 (row products); A007318.

Sequence in context: A292193 A258708 A113983 * A089980 A181031 A214987

Adjacent sequences:  A199330 A199331 A199332 * A199334 A199335 A199336

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Nov 09 2011

STATUS

approved

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Last modified September 19 17:50 EDT 2020. Contains 337180 sequences. (Running on oeis4.)