A093001 Least k such that Sum_{r=n+1..k} r is greater than or equal to the sum of the first n positive integers (i.e., the n-th triangular number, A000217(n)). Or, least k such that (sum of first n positive integers) <= (sum of numbers from n+1 up to k).

2, 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 45, 46, 47, 49, 50, 52, 53, 54, 56, 57, 59, 60, 62, 63, 64, 66, 67, 69, 70, 71, 73, 74, 76, 77, 78, 80, 81, 83, 84, 86, 87, 88, 90, 91, 93, 94, 95, 97, 98, 100, 101

Offset: 1

Author

Amarnath Murthy, Mar 29 2004

Keywords

• easy
• nonn

Examples

			a(6)= 9, 7+8+9 > 1+2+3+4+5+6, but 7+8 < 1+2+3+4+5+6.
		

Crossrefs

Cf. A093000.

Programs

Magma

[Ceiling((-1 + Sqrt(8*n^2 + 8*n + 1))/2): n in [1..80]]; // Vincenzo Librandi, Jul 23 2015

Mathematica

Table[Ceiling[(-1 + Sqrt[8 n^2 + 8 n + 1])/2], {n, 0, 80}] (* Vincenzo Librandi, Jun 23 2015 *)

PARI

a(n) = {my(k=1); while (sum(j=n+1, k, j) < n*(n+1)/2, k++); k;} \\ Michel Marcus, Jul 23 2015

Formula

a(n) = ceiling((-1 + sqrt(8n^2 + 8n + 1))/2). - Joshua Zucker, May 08 2006

Extensions

More terms from Joshua Zucker, May 08 2006