A085141 Greatest nonnegative integer k such that k(3k+1)/2 <= n.

0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8

Offset: 0

Author

Michael Somos, Jun 19 2003

Keywords

• nonn
• easy

Crossrefs

Cf. A005449.

Programs

PARI

a(n)=if(n<0,0,(sqrtint(24*n+1)-1)\6)

Formula

a(n) = floor((sqrt(24n+1)-1)/6).

a(A005449(n)) = n.