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Search: id:A094270
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| A094270 |
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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. |
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+0
5
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| 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
(list; table; graph; listen)
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OFFSET
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1,2
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LINKS
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Martin Fuller, Table of n, a(n) for n = 1..78
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FORMULA
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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 (mathar(AT)strw.leidenuniv.nl), Jun 23 2006
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EXAMPLE
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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 4-th row = 7*8*9*10 = 5040. Product of the terms of the 5-th row = 12*13*14*15*16 = 524160 = 104*5040.
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), Jun 23 2006
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CROSSREFS
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Cf. A094271, A094272, A094273, A094274.
Adjacent sequences: A094267 A094268 A094269 this_sequence A094271 A094272 A094273
Sequence in context: A004744 A072226 A074402 this_sequence A125705 A005524 A082918
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KEYWORD
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tabl,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 27 2004
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 23 2006
Further terms from Martin Fuller (martin_n_fuller(AT)btinternet.com), Jun 13 2007
Edited by njas, Jun 13 2007
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