A080820 Least m such that m^2 >= n*(n+1)/2.

1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 40, 41, 42, 43, 43, 44, 45, 45, 46, 47, 48, 48, 49, 50, 50, 51, 52, 52

Offset: 1

Author

Amarnath Murthy, Mar 21 2003

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A080817, A080818, A080819.

Programs

Maple

seq(ceil(sqrt(n*(n+1)/2)),n=1..80); # C. Ronaldo

Mathematica

lst = {}; m = 1; Do[While[n*(n + 1)/2 > m^2, m++]; AppendTo[lst, m], {n, 69}]; lst (* Arkadiusz Wesolowski, Jul 18 2012 *)
Ceiling[Sqrt[#]]&/@Accumulate[Range[80]] (* Harvey P. Dale, Feb 10 2016 *)

Formula

a(n) = A080819(n)^(1/2).

a(n) = ceiling(sqrt(n*(n+1)/2)) - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

Name changed by Arkadiusz Wesolowski, Jul 18 2012