A161205 Triangle read by rows in which row n lists 2n-1 followed by 2n numbers 2n.

1, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Author

Omar E. Pol, Jun 19 2009

Keywords

• easy
• nonn
• tabf

Comments

Row sums: A125202(n+1). - R. J. Mathar, Feb 16 2010

Examples

			Triangle begins:
  1,  2,  2;
  3,  4,  4,  4,  4;
  5,  6,  6,  6,  6,  6,  6;
  7,  8,  8,  8,  8,  8,  8,  8,  8;
  9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10;
		

Links

• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos
• Omar E. Pol, Illustration: Divisors and pi(x)

Crossrefs

Cf. A000005, A000720, A018253, A125202, A160811, A160812, A161339.

Programs

Maple

A161205 := proc(n,k) if k=1 then 2*n-1; else 2*n; end if; end proc: seq(seq(A161205(n,k),k=1..2*n+1),n=1..12) ; # R. J. Mathar, Feb 16 2010

Formula

If n is a perfect square, then a(n) = 2*sqrt(n)-1; otherwise a(n) = 2*floor(sqrt(n)). - Nathaniel Johnston, May 06 2011

a(n) = A000196(n-1) + A000196(n) = floor(sqrt(n-1)) + floor(sqrt(n)). - Ridouane Oudra, Jun 07 2019

Extensions

More terms from R. J. Mathar, Feb 16 2010