A253181 - OEIS

%I #23 May 05 2021 13:40:17

%S 1,2,3,4,5,9,13,15,16,17,25,32,35,36,37,40,43,46,49,52,56,63,64,65,81,

%T 99,100,101,109,121,136,143,144,145,152,158,169,175,190,195,196,197,

%U 225,243,255,256,257,289,312,317,323,324,325,331,336,351,356,361,366,377

%N Numbers n such that the distance between n^3 and the nearest square is less than n.

%C Distance can be zero, that is, cubes that are squares are included.

%C Numbers n such that A002938(n) < n.

%H Daniel Mondot, <a href="/A253181/b253181.txt">Table of n, a(n) for n = 1..10000</a>

%e The distance between 5^3=125 and the nearest square 11^2=121 is less than 5, so 5 is in the sequence.

%t dnsQ[n_]:=Module[{n3=n^3,sr},sr=Sqrt[n3];Min[n3-Floor[sr]^2, Ceiling[ sr]^2- n3]<n]; Select[Range[400],dnsQ] (* _Harvey P. Dale_, Dec 23 2015 *)

%o (Python)

%o def isqrt(a):

%o     sr = 1 << (int.bit_length(int(a)) >> 1)

%o     while a < sr*sr:  sr>>=1

%o     b = sr>>1

%o     while b:

%o         s = sr + b

%o         if a >= s*s:  sr = s

%o         b>>=1

%o     return sr

%o for n in range(1000):

%o     cube = n*n*n

%o     r = isqrt(cube)

%o     sqr = r**2

%o     if cube-sqr < n or sqr+2*r+1-cube < n:  print(str(n), end=',')

%Y Cf. A000290, A000578, A002760.

%Y Cf. A116885, A002938, A077119.

%Y Cf. A268509, A268510.

%K nonn

%O 1,2

%A _Alex Ratushnyak_, Mar 23 2015