A279431 -id:A279431 - cp's OEIS frontend

A280648 Numbers k such that k^3 has an odd number of digits and the middle digit is 8.

2, 24, 35, 38, 120, 127, 131, 138, 145, 172, 174, 182, 183, 208, 212, 215, 471, 481, 482, 485, 495, 505, 516, 517, 544, 551, 567, 594, 601, 610, 617, 621, 644, 646, 674, 677, 689, 736, 739, 749, 756, 768, 773, 774, 775, 776, 786, 799, 803, 812, 821, 830, 835

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 8, 13824, 42875, 54872, 1728000, 2048383, 2248091, 2628072, ...

			2^3 = (8), 172^3 = 508(8)448, 610^3 = 2269(8)1000.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640-A280647, A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

Select[Range[835], OddQ[len=Length[IntegerDigits[#^3]]]&&Part[IntegerDigits[#^3], (len+1)/2]==8 &] (* Stefano Spezia, Oct 03 2023 *)

A280650 Numbers k such that k^3 has an odd number of digits in base 2 and the middle digit is 0.

Original entry on oeis.org

0, 3, 4, 12, 16, 17, 29, 30, 31, 43, 44, 46, 48, 50, 64, 65, 68, 78, 79, 80, 102, 104, 105, 107, 108, 109, 112, 114, 116, 117, 118, 121, 127, 163, 167, 169, 170, 172, 173, 174, 175, 176, 179, 183, 186, 187, 188, 189, 191, 192, 193, 195, 196, 198, 200, 202, 203

Offset: 1

Lars Blomberg, Jan 12 2017

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

Lars Blomberg, Table of n, a(n) for n = 1..10000
Mail by Andrew Weimholt to the Seqfan Mailing list Dec 12 2016

Cf. A280651.
See A279430-A279431 for a k^2 version.
See A280640-A280649 for a base-10 version.
See A279420-A279429 for a k^2, base-10 version.

a[n_]:=Part[IntegerDigits[n, 2], (Length[IntegerDigits[n,2]] + 1)/2];
Select[Range[0, 203], OddQ[Length[IntegerDigits[#^3, 2]]] && a[#^3]==0 &] (* Indranil Ghosh, Mar 06 2017 *)
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 *)

isok(k) = my(d=digits(k^3, 2)); (#d%2 == 1) && (d[#d\2 +1] == 0);
for(k=0, 203, if(k==0 || isok(k)==1, print1(k,", "))); \\ Indranil Ghosh, Mar 06 2017

i=0
j=1
while i<=203:
    n=str(bin(i**3)[2:])
    l=len(n)
    if l%2==1 and n[(l-1)/2]=="0":
        print (str(i))+",",
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

A280651 Numbers k such that k^3 has an odd number of digits in base 2 and the middle digit is 1.

Original entry on oeis.org

1, 5, 7, 11, 18, 19, 20, 26, 27, 28, 41, 42, 45, 47, 49, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 103, 106, 110, 111, 113, 115, 119, 120, 122, 123, 124, 125, 126, 162, 164, 165, 166, 168, 171, 177, 178, 180, 181, 182, 184, 185, 190, 194, 197, 199, 201, 259

Offset: 1

Lars Blomberg, Jan 12 2017

			5^3 = 111(1)101_2, 28^3 = 1010101(1)1000000_2, 111^3 = 1010011011(1)1001001111_2.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Mail by Andrew Weimholt to the Seqfan Mailing list Dec 12 2016

Cf. A280650.
See A279430-A279431 for a k^2 version.
See A280640-A280649 for a base-10 version.
See A279420-A279429 for a k^2, base-10 version.

a[n_]:=Part[IntegerDigits[n,2],(Length[IntegerDigits[n,2]]+1)/2];
Select[Range[0, 259], OddQ[Length[IntegerDigits[#^3, 2]]] && a[#^3]==1 &] (* Indranil Ghosh, Mar 06 2017 *)
ond2Q[n_]:=Module[{idn=IntegerDigits[n^3,2],len},len=Length[idn];OddQ[ len] && idn[[(len+1)/2]]==1]; Select[Range[300],ond2Q] (* Harvey P. Dale, Jul 21 2021 *)

isok(k) = my(d=digits(k^3, 2)); (#d%2 == 1) && (d[#d\2 +1] == 1);
for(k=0, 259, if(isok(k)==1, print1(k,", "))); \\ Indranil Ghosh, Mar 06 2017

i=0
j=1
while i<=259:
    n=str(bin(i**3)[2:])
    l=len(n)
    if l%2==1 and n[(l-1)/2]=="1":
        print (str(i))+",",
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

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A280648 Numbers k such that k^3 has an odd number of digits and the middle digit is 8.

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A280650 Numbers k such that k^3 has an odd number of digits in base 2 and the middle digit is 0.

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A280651 Numbers k such that k^3 has an odd number of digits in base 2 and the middle digit is 1.

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Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python