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%I #7 May 01 2013 21:12:44
%S 1,2,3,5,7,10,14,18,22,27,33,39,45,52,60,68,76,85,95,105,115,126,138,
%T 150,162,175,189,202,217,232,247,263,280,297,314,332,351,370,389,409,
%U 430,451,472,494,517,540,563,587,612,637,662,688,715,741,769,797,825
%N Sum of a(n) terms of 1/sqrt(k) first strictly exceeds n.
%e Let b(k) = 1 + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(k):
%e .k.......1....2.....3.....4.....5.....6.....7
%e -------------------------------------------------
%e b(k)...1.00..1.71..2.28..2.78..3.23..3.64..4.01
%e For A019529 we have:
%e n=0: smallest k is a(0) = 1 since 1.00 > 0
%e n=1: smallest k is a(1) = 2 since 1.71 > 1
%e n=2: smallest k is a(2) = 3 since 2.28 > 2
%e n=3: smallest k is a(3) = 5 since 3.23 > 3
%e n=4: smallest k is a(4) = 7 since 4.01 > 4
%e For AA054040 we have:
%e n=1: smallest k is a(1) = 1 since 1.00 >= 1
%e n=2: smallest k is a(2) = 3 since 2.28 >= 2
%e n=3: smallest k is a(3) = 5 since 3.23 >= 3
%e n=4: smallest k is a(4) = 7 since 4.01 >= 4
%t s = 0; k = 1; Do[ While[ s <= n, s = s + N[ 1/Sqrt[ k ], 24 ]; k++ ]; Print[ k - 1 ], {n, 1, 75} ]
%Y A054040 is another version. See also A002387, A004080.
%K nonn
%O 0,2
%A _Robert G. Wilson v_
%E Edited by _N. J. A. Sloane_, Sep 01 2009
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