A102515 a(n) = floor(1 + sqrt(2n + 1)).

2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13

Offset: 0

Author

Giovanni Teofilatto, Mar 16 2005

Keywords

• easy
• nonn

Comments

The first occurrence of k appears at floor((k-1)^2/2), beginning with k=3. - Robert G. Wilson v, Mar 01 2015

If the sign inside the sqrt() is changed from "+" to "-", then the offset must be changed from 0 to 1 in order for the terms in the data to remain the same. - Robert G. Wilson v, Mar 01 2015

Programs

Mathematica

Table[Floor[1+Sqrt[2n+1]],{n,0,100}] (* Harvey P. Dale, Feb 28 2015 *)

Formula

With offset 1, a(n) = A339399(n) + A339443(n). - Wesley Ivan Hurt, Dec 31 2020

Extensions

Definition corrected by Olivier Gérard & Harvey P. Dale, Feb 28 2015

Offset corrected by Robert G. Wilson v, Mar 01 2015