A248164 -id:A248164 - cp's OEIS frontend

A098012 Triangle read by rows in which the k-th term in row n (n >= 1, k = 1..n) is Product_{i=0..k-1} prime(n-i).

2, 3, 6, 5, 15, 30, 7, 35, 105, 210, 11, 77, 385, 1155, 2310, 13, 143, 1001, 5005, 15015, 30030, 17, 221, 2431, 17017, 85085, 255255, 510510, 19, 323, 4199, 46189, 323323, 1616615, 4849845, 9699690, 23, 437, 7429, 96577, 1062347, 7436429, 37182145, 111546435, 223092870

Offset: 1

Alford Arnold, Sep 09 2004

Also, square array A(m,n) in which row m lists all products of m consecutive primes (read by falling antidiagonals). See also A248164. - M. F. Hasler, May 03 2017

			2
3 3*2
5 5*3 5*3*2
7 7*5 7*5*3 7*5*3*2
Or, as an infinite square array:
     2     3     5     7  ... : row 1 = A000040,
     6    15    35    77  ... : row 2 = A006094,
    30   105   385  1001  ... : row 3 = A046301,
   210  1155  5005 17017  ... : row 4 = A046302,
   ..., with col.1 = A002110, col.2 = A070826, col.3 = A059865\{1}. - _M. F. Hasler_, May 03 2017

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Cf. A000040, A002110, A006094, A046301, A046302, A046303.

Cf. A060381 (central terms), A104887, A248147.

P:=Filtered([1..200],IsPrime);;
T:=Flat(List([1..9],n->List([1..n],k->Product([0..k-1],i->P[n-i])))); # Muniru A Asiru, Mar 16 2019

a098012 n k = a098012_tabl !! (n-1) !! (k-1)
a098012_row n = a098012_tabl !! (n-1)
a098012_tabl = map (scanl1 (*)) a104887_tabl
-- Reinhard Zumkeller, Oct 02 2014

T:=(n,k)->mul(ithprime(n-i),i=0..k-1): seq(seq(T(n,k),k=1..n),n=1..9); # Muniru A Asiru, Mar 16 2019

Flatten[ Table[ Product[ Prime[i], {i, n, j, -1}], {n, 9}, {j, n, 1, -1}]] (* Robert G. Wilson v, Sep 21 2004 *)

T098012(n,k)=prod(i=0,k-1,prime(n-i)) \\ "Triangle" variant
A098012(m,n)=prod(i=0,m-1,prime(n+i)) \\ "Square array" variant. - M. F. Hasler, May 03 2017

n-th row = partial products of row n in A104887. - Reinhard Zumkeller, Oct 02 2014

More terms from Robert G. Wilson v, Sep 21 2004

A248147 Table read by rows: n-th row contains all consecutive subsets of the first n primes in their natural order.

Original entry on oeis.org

2, 2, 3, 2, 3, 2, 3, 5, 2, 3, 3, 5, 2, 3, 5, 2, 3, 5, 7, 2, 3, 3, 5, 5, 7, 2, 3, 5, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 11, 2, 3, 3, 5, 5, 7, 7, 11, 2, 3, 5, 3, 5, 7, 5, 7, 11, 2, 3, 5, 7, 3, 5, 7, 11, 2, 3, 5, 7, 11, 2, 3, 5, 7, 11, 13, 2, 3, 3, 5, 5, 7, 7, 11

Offset: 1

Reinhard Zumkeller, Oct 02 2014

A000292(n) = length of n-th row, whereas A000217(n) = number of all consecutive subsets of numbers 1..n;

T(n,k) = A000040(A248141(n,k)), 1 <= k <= A000292(n).

			.  1: 2
.  2: 2,3,2,3
.  3: 2,3,5,2,3,3,5,2,3,5
.  4: 2,3,5,7,2,3,3,5,5,7,2,3,5,3,5,7,2,3,5,7
.  5: 2,3,5,7,11,2,3,3,5,5,7,7,11,2,3,5,3,5,7,5,7,11,2,3,5,7,3,5,7,11,...
rows concatenated from:
.  1: [2]
.  2: [2] [3] [2,3]
.  3: [2] [3] [5] [2,3] [3,5] [2,3,5]
.  4: [2] [3] [5] [7] [2,3] [3,5] [5,7] [2,3,5] [3,5,7] [2,3,5,7]
.  5: [2] [3] [5] [7] [11] [2,3] [3,5] [5,7] [7,11] [2,3,5] [3,5,7] ...

Reinhard Zumkeller, Rows n = 1..20 of triangle, flattened

Cf. A151800, A000292, A000217, A248164, A248141.

import Data.List (group)
a248147 n k = a248147_tabf !! (n-1) !! (k-1)
a248147_row n = a248147_tabf !! (n-1)
a248147_tabf = map concat psss where
   psss = iterate f [[2]] where
      f pss = group (h $ last pss) ++ map h pss
      h ws = ws ++ [a151800 $ last ws]

cp's OEIS Frontend

A098012 Triangle read by rows in which the k-th term in row n (n >= 1, k = 1..n) is Product_{i=0..k-1} prime(n-i).

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