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

1,3

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000217, A186221.

Sequence in context: A368908 A100618 A248227 * A086525 A248231 A120503

Adjacent sequences: A061285 A061286 A061287 * A061289 A061290 A061291

Keyword

nonn,easy

Author

Amarnath Murthy, Apr 25 2001

Extensions

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

Status

approved