A064506 - OEIS

%I #9 Jun 20 2018 01:30:46

%S 0,1,2,2,3,4,4,5,6,6,7,8,9,9,10,11,11,12,13,14,14,15,16,16,17,18,18,

%T 19,20,21,21,22,23,23,24,25,26,26,27,28,28,29,30,30,31,32,33,33,34,35,

%U 35,36,37,38,38,39,40,40,41,42,42,43,44,45,45,46,47,47,48,49,50,50,51,52

%N a(n) = Max { k | k*(k+1)/2 <= n*(n+1)/2 - k*(k+1)/2 }.

%H Harry J. Smith, <a href="/A064506/b064506.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = floor((sqrt(2*n*(n+1) + 1) - 1) / 2)

%e 1+2+3+4+5 <= 6+7+8 and as 1+2+3+4+5+6 > 7+8 we have a(8) = 5.

%o (PARI) { for (n=1, 1000, a=(sqrt(2*n*(n + 1) + 1) - 1) \ 2; write("b064506.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 17 2009

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Oct 06 2001