A280641 Numbers k such that k^3 has an odd number of digits and the middle digit is 1.

1, 6, 8, 23, 44, 45, 102, 106, 110, 114, 117, 121, 137, 148, 152, 153, 162, 168, 176, 185, 189, 194, 206, 210, 478, 488, 512, 533, 553, 560, 574, 580, 626, 639, 655, 662, 669, 671, 676, 682, 683, 684, 685, 693, 704, 710, 730, 731, 737, 742, 758, 761, 767, 771

Offset

1,2

Comments

The sequence of cubes starts: 1, 216, 512, 12167, 85184, 91125, 1061208, 1191016, ...

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

1^3 = (1), 114^3 = 148(1)544, 560^3 = 1756(1)6000

Mathematica

a[n_]:=Part[IntegerDigits[n], (Length[IntegerDigits[n]] + 1)/2];
Select[Range[0, 771], OddQ[Length[IntegerDigits[#^3]]] && a[#^3]==1 &] (* Indranil Ghosh, Mar 06 2017 *)

Prog

(PARI)
isok(k) = my(d=digits(k^3)); (#d%2 == 1) && (d[#d\2 +1] == 1);
for(k=0, 771, if(isok(k)==1, print1(k, ", "))); \\ Indranil Ghosh, Mar 06 2017
(Python)
i=0
j=1
while i<=771:
    n=str(i**3)
    l=len(n)
    if l%2 and n[(l-1)//2]=="1":
        print(str(i), end=', ')
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

Crossrefs

Cf. A280640, A280642-A280649, A181354.

See A279420-A279429 for a k^2 version.

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

Sequence in context: A276226 A034761 A085796 * A005887 A349172 A119875

Adjacent sequences: A280638 A280639 A280640 * A280642 A280643 A280644

Keyword

nonn,base,easy

Author

Lars Blomberg, Jan 07 2017

Status

approved