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Search: id:A093000
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| A093000 |
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Least k such that Sum (r); r = n+1 to k is just >= n! Or least k such that product of first n numbers < sum of numbers beginning with n+1 up to k. |
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+0
2
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| 2, 3, 5, 8, 16, 38, 101, 284, 852, 2694, 8935, 30952, 111598, 417560, 1617204, 6468816, 26671611, 113158064, 493244565, 2205856753, 10108505545, 47413093714, 227385209453, 1113955476429, 5569777382146, 28400403557929
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Floor [Sqrt(2*n! + n^2)] for most values of n, the exceptions are 1,2,3,7,... in which case a(n) = Floor [Sqrt(2*n! + n^2)] + 1.
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FORMULA
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Least k such that {k(k+1)/2 - n(n+1)/2} >= n!
a(n) = ceiling[(-1 + sqrt(1 + 8n! + 4n^2 + 4n))/2] and ignoring the -1 outside the sqrt and + 1 inside gives the approximate formula in the comment. - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 08 2006
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EXAMPLE
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a(4) = 8, 5+6+7+8 = 26 >24, but 5+6+7=18, 24=4!
a(5) = 16, 6+7+8+...+15+16 = 121 > 120 = 5!
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PROGRAM
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(PARI) { for(n=1, 20, s=0; found=0; for(k=n+1, 10000000, if( k*(k+1)-n*(n+1)>= 2*n!, print1(k, ", "); found=1; break; ); ); if(found==0, print(0); ); ); } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 21 2006
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CROSSREFS
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Cf. A093001.
Sequence in context: A050295 A121649 A030034 this_sequence A122630 A108054 A123612
Adjacent sequences: A092997 A092998 A092999 this_sequence A093001 A093002 A093003
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KEYWORD
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easy,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 29 2004
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 21 2006
More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 08 2006
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