A181092 a(n) is the sum of n addends nested as follows: floor(sqrt(floor(sqrt(...(n)...)))).

1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80

Offset

1,2

Comments

a(n)=n+k(n) k has an increment of at least 1 unit when n is a perfect square.

The converse is not true:

Its complement is 4, 10, 18, 19, 29, 41, 55, 71, 89, 90, 110, 132, 156, 182, 210, 240, .... - Robert G. Wilson v, Nov 15 2012

Links

Carmine Suriano, Table of n, a(n) for n = 1..2010

Formula

a(n) = n + sqrt(n) + O(n^(1/4)). - Charles R Greathouse IV, Nov 15 2012

Example

a(5)=6 since floor(sqrt(5))=2; floor(sqrt(2))=1; floor(sqrt(1))=1 for the remaining three additional iterations.

Mathematica

f[n_] := Plus @@ Rest@ NestList[ Floor@ Sqrt@# &, n, n]; Array[f, 72] (* Robert G. Wilson v, Nov 15 2012 *)

Prog

(PARI) a(n)=my(k=n, s); while((n=sqrtint(n))>1, s+=n; k--); s+k \\ Charles R Greathouse IV, Nov 15 2012

Crossrefs

Cf. A219227.

Sequence in context: A247360 A145397 A183570 * A184526 A047256 A039252

Adjacent sequences: A181089 A181090 A181091 * A181093 A181094 A181095

Keyword

nonn,easy

Author

Carmine Suriano, Oct 02 2010

Status

approved