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A098012
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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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4
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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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:
30 105 385 1001 ... : row 3 = A046301,
210 1155 5005 17017 ... : row 4 = A046302,
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MAPLE
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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
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MATHEMATICA
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Flatten[ Table[ Product[ Prime[i], {i, n, j, -1}], {n, 9}, {j, n, 1, -1}]] (* Robert G. Wilson v, Sep 21 2004 *)
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PROG
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(Haskell)
a098012 n k = a098012_tabl !! (n-1) !! (k-1)
a098012_row n = a098012_tabl !! (n-1)
a098012_tabl = map (scanl1 (*)) a104887_tabl
(PARI) 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
(GAP) 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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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