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 A093000 Least k such that Sum_{r=n+1..k} r >= n!. 1
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, least k such that the product of the first n positive integers is less than the sum of the integers from n+1 through k. a(n) = 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. LINKS FORMULA 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 the 1 inside gives the approximate formula in the comment. - Joshua Zucker, May 08 2006 EXAMPLE a(4) = 8 because 4! = 24 and 5+6+7+8 = 26 > 24, but 5+6+7 = 18. a(5) = 16 because 5! = 120 and 6+7+8+...+15+16 = 121 > 120. PROG (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, Apr 21 2006 CROSSREFS Cf. A093001. Sequence in context: A306622 A030034 A308852 * A122630 A108054 A123612 Adjacent sequences:  A092997 A092998 A092999 * A093001 A093002 A093003 KEYWORD easy,nonn AUTHOR Amarnath Murthy, Mar 29 2004 EXTENSIONS More terms from R. J. Mathar, Apr 21 2006 More terms from Joshua Zucker, May 08 2006 Name simplified by Jon E. Schoenfield, Jun 15 2019 STATUS approved

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Last modified October 28 13:26 EDT 2020. Contains 338055 sequences. (Running on oeis4.)