A280650 - OEIS

%I #15 Dec 23 2024 14:53:45

%S 0,3,4,12,16,17,29,30,31,43,44,46,48,50,64,65,68,78,79,80,102,104,105,

%T 107,108,109,112,114,116,117,118,121,127,163,167,169,170,172,173,174,

%U 175,176,179,183,186,187,188,189,191,192,193,195,196,198,200,202,203

%N Numbers k such that k^3 has an odd number of digits in base 2 and the middle digit is 0.

%H Lars Blomberg, <a href="/A280650/b280650.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2016-December/017140.html">Mail by Andrew Weimholt to the Seqfan Mailing list Dec 12 2016</a>

%e 3^3 = 11(0)11_2, 43^3 = 10011011(0)10010011_2, 117^3 = 1100001110(0)0001001101_2.

%t a[n_]:=Part[IntegerDigits[n, 2], (Length[IntegerDigits[n,2]] + 1)/2];

%t Select[Range[0, 203], OddQ[Length[IntegerDigits[#^3, 2]]] && a[#^3]==0 &] (* _Indranil Ghosh_, Mar 06 2017 *)

%t md0Q[n_]:=Module[{idn2=IntegerDigits[n^3,2],len},len=Length[idn2];OddQ[ len] &&idn2[[(len+1)/2]]==0]; Select[Range[0,250],md0Q] (* _Harvey P. Dale_, Dec 15 2019 *)

%o (PARI) isok(k) = my(d=digits(k^3, 2)); (#d%2 == 1) && (d[#d\2 +1] == 0);

%o for(k=0, 203, if(k==0 || isok(k)==1, print1(k,", "))); \\ _Indranil Ghosh_, Mar 06 2017

%o (Python)

%o i=0

%o j=1

%o while i<=203:

%o ....n=str(bin(i**3)[2:])

%o ....l=len(n)

%o ....if l%2==1 and n[(l-1)/2]=="0":

%o ........print (str(i))+",",

%o ........j+=1

%o ....i+=1 # _Indranil Ghosh_, Mar 06 2017

%Y Cf. A280651.

%Y See A279430-A279431 for a k^2 version.

%Y See A280640-A280649 for a base-10 version.

%Y See A279420-A279429 for a k^2, base-10 version.

%K nonn,base,easy

%O 1,2

%A _Lars Blomberg_, Jan 12 2017