A064506 a(n) = Max { k | k*(k+1)/2 <= n*(n+1)/2 - k*(k+1)/2 }.

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, 19, 20, 21, 21, 22, 23, 23, 24, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 47, 48, 49, 50, 50, 51, 52

Offset

1,3

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

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

Example

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

Prog

(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

Crossrefs

Sequence in context: A094331 A135672 A265133 * A082774 A074239 A248333

Adjacent sequences: A064503 A064504 A064505 * A064507 A064508 A064509

Keyword

nonn

Author

Reinhard Zumkeller, Oct 06 2001

Status

approved