A061288 Integer part of square root of n-th triangular number.

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

Offset: 1

Author

Amarnath Murthy, Apr 25 2001

Keywords

• nonn
• easy

Examples

			a(10) = 7, the 10th triangular number is 55 and floor(sqrt(55)) = floor(7.4161) = 7.
		

Links

• Winston de Greef, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A186221.

Programs

Maple

for n from 1 to 150 do printf("%d,",floor(sqrt(n*(n+1)/2))) od;

Mathematica

Table[Floor[Sqrt[n*(n + 1)/2]], {n, 100}] (* Zak Seidov, May 25 2015 *)
IntegerPart[Sqrt[#]]&/@Accumulate[Range[80]] (* Harvey P. Dale, May 13 2018 *)

PARI

{a(n) = sqrtint(n * (n+1) \ 2)}; /* Michael Somos, Aug 19 2018 */

Formula

a(n) = floor(sqrt(n*(n+1)/2)). - Zak Seidov, May 25 2015

a(n) = a(-1-n) = A186221(n) - n for all n in Z. - Michael Somos, Aug 19 2018

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), May 07 2001