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%I #30 Aug 05 2023 23:51:36
%S 2,5,8,13,19,25,33,42,51,62,74,86,100,115,130,147,165,183,203,224,245,
%T 268,292,316,342,369,396,425,455,485,517,550,583,618,654,690,728,767,
%U 806,847,889,931,975,1020,1065,1112,1160,1208,1258,1309,1360,1413,1467
%N Least k such that 1+2+...+k >= E{1,2,...,n}, where E = 2nd elementary symmetric function.
%F G.f.: x^2 * (x+2) / ((1-x^3)*(1-x)^2).
%F a(n) = A000217(n+1) + (A049347(n) - 4*(n+1))/3. - _R. J. Mathar_, Aug 18 2008
%F Conjecture: a(n) = n + (n^2 mod 3) + a(n-1). - _Jon Maiga_, Aug 02 2019
%F 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
%t Table[Total[Table[IntegerExponent[2^(n - k) 4^k, 8], {k, 0, n}]], {n, 2, 100}] (* _Fred Daniel Kline_, Jun 05 2012 *)
%Y Cf. A000217, A000914, A049347.
%K nonn
%O 2,1
%A _Clark Kimberling_
%E Extended according to the g.f. by _R. J. Mathar_, Aug 18 2008
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