login
A027916
Least k such that 1+2+...+k >= E{1,2,...,n}, where E = 2nd elementary symmetric function.
1
2, 5, 8, 13, 19, 25, 33, 42, 51, 62, 74, 86, 100, 115, 130, 147, 165, 183, 203, 224, 245, 268, 292, 316, 342, 369, 396, 425, 455, 485, 517, 550, 583, 618, 654, 690, 728, 767, 806, 847, 889, 931, 975, 1020, 1065, 1112, 1160, 1208, 1258, 1309, 1360, 1413, 1467
OFFSET
2,1
FORMULA
G.f.: x^2 * (x+2) / ((1-x^3)*(1-x)^2).
a(n) = A000217(n+1) + (A049347(n) - 4*(n+1))/3. - R. J. Mathar, Aug 18 2008
Conjecture: a(n) = n + (n^2 mod 3) + a(n-1). - Jon Maiga, Aug 02 2019
a(n) = ceiling((1/2)*(sqrt(3*n^4 + 2*n^3 - 3*n^2 - 2*n + 3)/sqrt(3) - 1)) = (3*n+4)*(n-1)/6 + ((n+2) mod 3)/3. - Rick Mabry, Jul 01 2023
MATHEMATICA
Table[Total[Table[IntegerExponent[2^(n - k) 4^k, 8], {k, 0, n}]], {n, 2, 100}] (* Fred Daniel Kline, Jun 05 2012 *)
CROSSREFS
KEYWORD
nonn
EXTENSIONS
Extended according to the g.f. by R. J. Mathar, Aug 18 2008
STATUS
approved