A007069 - OEIS

%I M1329 #34 Aug 30 2022 02:11:18

%S 1,2,5,7,9,11,12,15,16,19,21,22,25,26,29,31,33,35,36,39,41,43,45,46,

%T 49,50,53,55,57,59,60,63,65,67,69,70,73,74,77,79,80,83,84,87,89,91,93,

%U 94,97,98,101,103,104,107,108,111,113,115,117,118,121,123,125,127,128,131

%N First column of spectral array W(sqrt 2).

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

%H G. C. Greubel, <a href="/A007069/b007069.txt">Table of n, a(n) for n = 1..10000</a>

%H A. Fraenkel and C. Kimberling, <a href="http://dx.doi.org/10.1016/0012-365X(94)90259-3">Generalized Wythoff arrays, shuffles and interspersions</a>, Discrete Mathematics 126 (1994) 137-149.

%F From _Benoit Cloitre_, Apr 06 2003: (Start)

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

%F a(n) = A001951(A001951(n)).

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

%t Table[Floor[Sqrt[2]*Floor[Sqrt[2]*n]], {n, 1, 100}] (* _G. C. Greubel_, Aug 16 2018 *)

%o (PARI) vector(100,n, floor(sqrt(2)*floor(n*sqrt(2)))) \\ _G. C. Greubel_, Aug 16 2018

%o (Magma) [Floor(Sqrt(2)*Floor(Sqrt(2)*n)): n in [1..100]]; // _G. C. Greubel_, Aug 16 2018

%o (Python)

%o from math import isqrt

%o def A007069(n): return isqrt(isqrt(n**2<<1)**2<<1) # _Chai Wah Wu_, Aug 29 2022

%Y Cf. A001951, A059648.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, _Mira Bernstein_

%E More terms from _Benoit Cloitre_, Apr 06 2003