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A285056 a(n) = the first positive integer, not ending in zero, whose cube has a substring of exactly n identical digits. 1
1, 11, 126, 753, 1923, 32183, 134708, 1487139, 23908603, 215443469, 106917811, 15056809703, 27354803113, 681048619195, 361160395301 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..15.

EXAMPLE

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

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 *)

PROG

(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).

CROSSREFS

Cf. A167712.

Sequence in context: A240335 A076483 A209901 * A015597 A296732 A156970

Adjacent sequences:  A285053 A285054 A285055 * A285057 A285058 A285059

KEYWORD

nonn,base,more

AUTHOR

Jason Wang, Apr 08 2017

EXTENSIONS

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

STATUS

approved

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Last modified September 18 07:39 EDT 2020. Contains 337166 sequences. (Running on oeis4.)