A285056 a(n) = the first positive integer, not ending in zero, whose cube has a substring of exactly n identical digits.

1, 11, 126, 753, 1923, 32183, 134708, 1487139, 23908603, 215443469, 106917811, 15056809703, 27354803113, 681048619195, 361160395301

Offset: 1

Author

Jason Wang, Apr 08 2017

Keywords

• nonn
• base
• more

Examples

			a(3) = 126, as 126^3 = 2000376 contains a digit (0) repeated n (3) times.
		

Crossrefs

Cf. A167712.

Programs

Mathematica

a[n_] := Block[{k=1}, While[Mod[k, 10] == 0 || ! MemberQ[Length /@ Split[ IntegerDigits[ k^3]], n], k++]; k]; Array[a, 8] (* Giovanni Resta, Apr 10 2017 *)

Python

import collections
import re
cur = 1
def repeat( num , reps ):
    r = str(num)
    n = 1
    while n < reps:
        r += str(num)
        n += 1
    return r;
while True:
    k = 0
    while k < 10:
        rep = repeat(k,9)
        while re.search(rep, str(cur**3)) != None:
            if re.search(rep + str(k), str(cur**3)) == None:
                print(str(cur) + ", " + str(cur**3))
                rep += str(k)
            else:
                rep += str(k)
        k += 1
    cur += 1
    if cur % 10 == 0:
        cur += 1 #note: this will display all cubes with a substring of 9 repeated digits. To change this to n repeats, replace repeat(k,9) with repeat(k,n).

Extensions

a(10)-a(15) from Giovanni Resta, Apr 10 2017