A007069 First column of spectral array W(sqrt 2).

1, 2, 5, 7, 9, 11, 12, 15, 16, 19, 21, 22, 25, 26, 29, 31, 33, 35, 36, 39, 41, 43, 45, 46, 49, 50, 53, 55, 57, 59, 60, 63, 65, 67, 69, 70, 73, 74, 77, 79, 80, 83, 84, 87, 89, 91, 93, 94, 97, 98, 101, 103, 104, 107, 108, 111, 113, 115, 117, 118, 121, 123, 125, 127, 128, 131

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• A. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discrete Mathematics 126 (1994) 137-149.

Crossrefs

Cf. A001951, A059648.

Programs

Magma

[Floor(Sqrt(2)*Floor(Sqrt(2)*n)): n in [1..100]]; // G. C. Greubel, Aug 16 2018

Mathematica

Table[Floor[Sqrt[2]*Floor[Sqrt[2]*n]], {n, 1, 100}] (* G. C. Greubel, Aug 16 2018 *)

PARI

vector(100,n, floor(sqrt(2)*floor(n*sqrt(2)))) \\ G. C. Greubel, Aug 16 2018

Python

from math import isqrt
def A007069(n): return isqrt(isqrt(n**2<<1)**2<<1) # Chai Wah Wu, Aug 29 2022

Formula

From Benoit Cloitre, Apr 06 2003: (Start)

Iterated floor function: a(n) = floor(sqrt(2)*floor(sqrt(2)*n)).

a(n) = A001951(A001951(n)).

a(n) = 2*n - 1 - A059648(n). (End)

Extensions

More terms from Benoit Cloitre, Apr 06 2003