A280642 Numbers k such that k^3 has an odd number of digits and the middle digit is 2.

5, 9, 103, 113, 133, 146, 151, 154, 165, 180, 198, 202, 470, 473, 493, 496, 504, 507, 521, 531, 538, 542, 566, 569, 581, 591, 593, 599, 612, 618, 620, 650, 654, 673, 681, 686, 703, 711, 715, 728, 729, 732, 740, 779, 801, 829, 841, 850, 855, 856, 857, 858, 874

Offset

1,1

Comments

The sequence of cubes starts: 125, 729, 1092727, 1442897, 2352637, 3112136, 3442951, 3652264, ...

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

5^3 = 1(2)5, 180^3 = 583(2)000, 618^3 = 2360(2)9032.

Mathematica

a[n_]:=Part[IntegerDigits[n], (Length[IntegerDigits[n]]+1)/2];
Select[Range[0, 874], OddQ[Length[IntegerDigits[#^3]]] && a[#^3]==2 &] (* Indranil Ghosh, Mar 06 2017 *)

Prog

(PARI)
isok(k) = my(d=digits(k^3)); (#d%2 == 1) && (d[#d\2 +1] == 2);
for(k=0, 874, if(isok(k)==1, print1(k, ", "))); \\ Indranil Ghosh, Mar 06 2017
(Python)
i=0
j=1
while i<=874:
    n=str(i**3)
    l=len(n)
    if l%2 and n[(l-1)//2]=="2":
        print(str(i), end=', ')
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

Crossrefs

Cf. A280640-A280641, A280643-A280649, A181354.

See A279420-A279429 for a k^2 version.

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

Sequence in context: A098097 A279707 A329002 * A359396 A222583 A222374

Adjacent sequences: A280639 A280640 A280641 * A280643 A280644 A280645

Keyword

nonn,base,easy,changed

Author

Lars Blomberg, Jan 07 2017

Status

approved