A097046 a(n) = a(n-1) + a(floor(sqrt(n))) for n > 1; a(1) = 1.

1, 2, 3, 5, 7, 9, 11, 13, 16, 19, 22, 25, 28, 31, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 86, 93, 100, 107, 114, 121, 128, 135, 142, 149, 156, 165, 174, 183, 192, 201, 210, 219, 228, 237, 246, 255, 264, 273, 284, 295, 306, 317, 328, 339, 350, 361, 372, 383, 394, 405

Offset: 1

Author

Rick L. Shepherd, Jul 20 2004

Keywords

• nonn

Comments

By definition, this sequence consists of an infinite sequence of finite subsequences of increasing lengths with common differences a(1), a(2), a(3), ..., respectively.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A097045 ( a(n-1) - a(floor(sqrt(n))) ).

Programs

Maple

a:= proc(n) option remember;
     `if`(n<2, 1, a(n-1)+a(floor(sqrt(n))))
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, Apr 09 2021

Formula

a(1)=1; a(n) = a(n-1) + a(floor(sqrt(n))) for n > 1.