A094270 Triangle read by rows: row n contains the least set of n successive numbers whose product is a multiple of the product of the previous row. The first term of each row must be larger than the last term of the previous row.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 47, 48, 49, 50, 51, 52, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 687371, 687372, 687373, 687374, 687375, 687376, 687377, 687378, 236241851618, 236241851619, 236241851620, 236241851621

Offset

1,2

Links

Martin Fuller, Table of n, a(n) for n = 1..78

Formula

product{k=1,..,n} a(n,k) | product{k=1,..,n+1} a(n+1,k). a(n,k+1)=a(n,k)+1 for k=1,..,n-1. a(n,1)>a(n-1,n-1). - R. J. Mathar, Jun 23 2006

Example

Triangle begins:
1
2 3
4 5 6
7 8 9 10
12 13 14 15 16
47 48 49 50 51 52
Product of the terms of the 4th row = 7*8*9*10 = 5040. Product of the terms of the 5th row = 12*13*14*15*16 = 524160 = 104*5040.

Maple

A094270 := proc(nmax) local a, k, strt, aproo, apro, i, j, s; a := array(1..nmax, 1..nmax); a[1, 1] := 1; print(a[1, 1]); k := 2; while k < nmax do strt := a[k-1, k-1]+1; aproo := product(a[k-1, i], i=1..k-1); while true do apro := product(strt+j-1, j=1..k); if ( apro mod aproo ) =0 then for s from 1 to k do a[k, s] := strt+s-1; print(a[k, s]); od; break; fi; strt := strt+1; od; k := k+1; od; RETURN(a); end: A094270(10) : # R. J. Mathar, Jun 23 2006

Crossrefs

Cf. A094271, A094272, A094273, A094274.

Sequence in context: A233264 A198343 A342382 * A125705 A154314 A239348

Adjacent sequences: A094267 A094268 A094269 * A094271 A094272 A094273

Keyword

tabl,nonn

Author

Amarnath Murthy, Apr 27 2004

Extensions

More terms from R. J. Mathar, Jun 23 2006

Further terms from Martin Fuller, Jun 13 2007

Edited by N. J. A. Sloane, Jun 13 2007

Status

approved