A238598 Largest integer k such that n >= k^2-k-1 = A165900(k).

1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 0

Author

M. F. Hasler, Mar 01 2014

Keywords

• nonn

Comments

Also: Truncation to the integer part of the inverse function of A165900 = x -> x^2-x-1 (strictly increasing for x > 1/2): a(n) = floor(g(n)), where g = A165900^{-1}.

A left inverse of A165900 on the positive integers: a(A165900(n)) = n for all n>0.

Programs

PARI

A238598(n)=ceil(sqrtint(4*n+8)/2)-(n==1)

Formula

a(n) = A000194(n+2) - [n=1], where [P]=1 if P is true, [P]=0 else.