A168341 The lexicographically earliest injective sequence of nonnegative integers such that a(a(n)) is a square for all n>=0.

0, 1, 3, 4, 9, 6, 16, 8, 25, 36, 11, 49, 13, 64, 15, 81, 100, 18, 121, 20, 144, 22, 169, 24, 196, 225, 27, 256, 29, 289, 31, 324, 33, 361, 35, 400, 441, 38, 484, 40, 529, 42, 576, 44, 625, 46, 676, 48, 729, 784, 51, 841, 53, 900, 55, 961, 57, 1024, 59, 1089, 61, 1156, 63

Offset

0,3

Comments

The term a(n) is either n+1 or a square. All the squares appear and they appear in increasing order. Every other term is a square, except when the index is a square, in which case, the corresponding term is also a square (which shifts the pattern). See FORMULA for a more precise statement.

Links

Table of n, a(n) for n=0..62.

Formula

To define a(n), let k = floor(sqrt(n)). Then a(n) = n+1 if n-k^2 is odd and ((n+k)/2)^2 if n-k^2 is even.

Note that k^2 is the largest square which is at most n.

Example

For n=6, we have k=floor(sqrt(6))=2; since 6-2=4 is even, a(6)=((6+2)/2)^2=16.

Crossrefs

Sequence in context: A337180 A003959 A344461 * A083111 A354112 A345270

Adjacent sequences: A168338 A168339 A168340 * A168342 A168343 A168344

Keyword

nonn

Author

Eric Angelini and Benoit Jubin, Nov 23 2009

Status

approved