A098012 - OEIS

%I #22 Mar 16 2019 12:09:46

%S 2,3,6,5,15,30,7,35,105,210,11,77,385,1155,2310,13,143,1001,5005,

%T 15015,30030,17,221,2431,17017,85085,255255,510510,19,323,4199,46189,

%U 323323,1616615,4849845,9699690,23,437,7429,96577,1062347,7436429,37182145,111546435,223092870

%N 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).

%C 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

%H Reinhard Zumkeller, <a href="/A098012/b098012.txt">Rows n = 1..125 of triangle, flattened</a>

%F n-th row = partial products of row n in A104887. - _Reinhard Zumkeller_, Oct 02 2014

%e 2

%e 3 3*2

%e 5 5*3 5*3*2

%e 7 7*5 7*5*3 7*5*3*2

%e Or, as an infinite square array:

%e      2     3     5     7  ... : row 1 = A000040,

%e      6    15    35    77  ... : row 2 = A006094,

%e     30   105   385  1001  ... : row 3 = A046301,

%e    210  1155  5005 17017  ... : row 4 = A046302,

%e    ..., with col.1 = A002110, col.2 = A070826, col.3 = A059865\{1}. - _M. F. Hasler_, May 03 2017

%p 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

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

%o (Haskell)

%o a098012 n k = a098012_tabl !! (n-1) !! (k-1)

%o a098012_row n = a098012_tabl !! (n-1)

%o a098012_tabl = map (scanl1 (*)) a104887_tabl

%o -- _Reinhard Zumkeller_, Oct 02 2014

%o (PARI) T098012(n,k)=prod(i=0,k-1,prime(n-i)) \\ "Triangle" variant

%o A098012(m,n)=prod(i=0,m-1,prime(n+i)) \\ "Square array" variant. - _M. F. Hasler_, May 03 2017

%o (GAP) P:=Filtered([1..200],IsPrime);;

%o T:=Flat(List([1..9],n->List([1..n],k->Product([0..k-1],i->P[n-i])))); # _Muniru A Asiru_, Mar 16 2019

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

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

%K easy,nonn,tabl

%O 1,1

%A _Alford Arnold_, Sep 09 2004

%E More terms from _Robert G. Wilson v_, Sep 21 2004