A280640 Numbers k such that k^3 has an odd number of digits and the middle digit is 0.

0, 30, 40, 42, 100, 101, 115, 116, 123, 126, 135, 163, 164, 171, 199, 200, 201, 214, 468, 479, 487, 498, 500, 502, 513, 520, 525, 543, 557, 562, 564, 575, 576, 577, 578, 579, 585, 596, 600, 615, 623, 642, 656, 661, 666, 690, 695, 697, 700, 705, 709, 717, 721

Offset

1,2

Comments

The sequence of cubes starts: 0, 27000, 64000, 74088, 1000000, 1030301, 1520875, 1560896, ...

Links

Lars Blomberg, Table of n, a(n) for n = 1..10000

Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Example

0^3 = (0), 126^3 = 200(0)376, 562^3 = 1775(0)4328.

Mathematica

a[n_]:=Part[IntegerDigits[n], (Length[IntegerDigits[n]] + 1)/2];
Select[Range[0, 721], OddQ[Length[IntegerDigits[#^3]]] && a[#^3]==0 &] (* Indranil Ghosh, Mar 06 2017 *)

Prog

(PARI)
isok(k) = my(d=digits(k^3)); (#d%2 == 1) && (d[#d\2 +1] == 0);
for(k=0, 721, if(k==0 || isok(k)==1, print1(k, ", "))); \\ Indranil Ghosh, Mar 06 2017
(Python)
i=0
j=1
while i<=721:
    n=str(i**3)
    l=len(n)
    if l%2 and n[(l-1)//2]=="0":
        print(str(i), end=", ")
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

Crossrefs

Cf. A280641-A280649, A181354.

See A279420-A279429 for a k^2 version.

See A279430-A279431 for a k^2 version in base 2.

Sequence in context: A004433 A223727 A025376 * A152616 A309306 A103250

Adjacent sequences: A280637 A280638 A280639 * A280641 A280642 A280643

Keyword

nonn,base,easy

Author

Lars Blomberg, Jan 07 2017

Status

approved