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

1,2

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

Formula

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

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

Crossrefs

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

Sequence in context: A287374 A186390 A022554 * A248420 A011861 A229511

Adjacent sequences: A097043 A097044 A097045 * A097047 A097048 A097049

Keyword

nonn

Author

Rick L. Shepherd, Jul 20 2004

Status

approved