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Search: id:A092935
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| A092935 |
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a(1) = 1; a(n) = floor {(n+1)(n+2)(n+3)...(n+k)}/{(n-1)(n-2)(n-3)...(n-k)} for the least value of k. |
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+0
2
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| 1, 3, 2, 5, 14, 42, 6, 429, 1430, 4862, 16796, 58786, 2261, 742900, 2674440, 66861, 35357670, 129644790, 2274470, 1767263190, 25246617, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The first occurrence of an integer in the sequence (n+1)/(n-1), (n+1)(n+2)/{(n-1)(n-2)}, (n+1)(n+2)(n+3)/{(n-1)(n-2)(n-3)},... The triangle of these numbers with initial value of n = 2, for k = 1 to n-1 is:
3
2 10
5/3 5 35
3/2 7/2 14 126
7/5 14/5 42/5 42 462
4/3 12/5 6 22 132 1716
...
Sequence contains the first integer in each row.
The leading diagonal of the triangle is given by A001700 = C(2n+1,n+1). i.e. eventually an integer occurs for k < n-1.
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EXAMPLE
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a(6)= 42: the relevant numbers are 7/5, 7*8/(5*4), 7*8*9/(5*4*3), (7*8*9*10)/(5*4*3*2),...or 1.4, 2.8,8.4,42,...
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PROGRAM
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(PARI) { a(n) = local(p, q, r); p=1; q=1; for(k=1, n, p*=n+k; q*=n-k; r=gcd(p, q); p\=r; q\=r; if(q==1, break)); return(p) } (Alekseyev)
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CROSSREFS
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Cf. A001700.
Sequence of corresponding values of k is A103634
Sequence in context: A075146 A062941 A057674 this_sequence A137455 A111273 A068553
Adjacent sequences: A092932 A092933 A092934 this_sequence A092936 A092937 A092938
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 22 2004
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EXTENSIONS
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More terms from Max Alekseyev (maxale(AT)gmail.com), Feb 11 2005
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