cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 25 results. Next

A215732 a(n) is the first digit to appear n times in succession in a power of 2.

Original entry on oeis.org

1, 5, 7, 5, 6, 8, 7, 1, 9, 9, 6, 3, 2, 9, 1, 4, 1
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Comments

Assumes that there are no 2 digits that appear n times in succession for the first time in the same power of 2. - Chai Wah Wu, Apr 26 2019

Examples

			2^16 = 65536 is the first power of 2 with a repeated digit (cf. A045875), with 5 repeated, so a(2) = 5. - _N. J. A. Sloane_, Aug 23 2012
		

Crossrefs

Programs

  • Mathematica
    n = 1; x = 1; lst = {};
    For[i = 1, i <= 10000, i++,
    z = Split[IntegerDigits[x]]; a = Length /@ z; b = Max[a];
    For[j = n, j <= b, j++,
      AppendTo[lst, First[First[Part[z, First[Position[a, b]]]]]]; n++
    ]; x = 2 x ]; lst (* Robert Price, Mar 16 2019 *)
  • Python
    def A215732(n):
        l, x = [str(d)*n for d in range(10)], 1
        for m in range(10**9):
            s = str(x)
            for k in range(10):
                if l[k] in s:
                    return k
            x *= 2
        return 'search limit reached'
    # Chai Wah Wu, Dec 17 2014

Extensions

a(11)-a(13) added by T. D. Noe, Sep 04 2012
a(14) added by T. D. Noe, Sep 06 2012
a(15) from Bert Dobbelaere, Feb 25 2019
a(16) from Paul Geneau de Lamarlière, Jun 26 2024
a(17) from Paul Geneau de Lamarlière, Sep 24 2024

A215727 a(n) is the smallest m for which 3^m contains n consecutive identical digits.

Original entry on oeis.org

0, 11, 32, 33, 274, 538, 2124, 7720, 22791, 107187, 107187, 639226, 5756979, 8885853, 68353787, 78927180, 78927180
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Comments

3^(a(16)+1) contains exactly 16 consecutive 3's. - Bert Dobbelaere, Mar 20 2019

Examples

			3^11 = 177147, which has two digits in a row.
		

Crossrefs

Programs

  • Mathematica
    A215727[n_] := Module[{m = 0 , t}, t = Table[i, {i, 0, 9}, {n}];
    While[True, If[ContainsAny[Subsequences[IntegerDigits[3^m], {n}], t], Return[m], m++]]; m]; Table[A215727[n], {n, 1, 14}] (* Robert Price, Oct 16 2018 *)
  • Python
    def A215727(n):
        l, x = [str(d)*n for d in range(10)], 1
        for m in range(10**9):
            s = str(x)
            for k in l:
                if k in s:
                    return m
            x *= 3
        return 'search limit reached'
    # Chai Wah Wu, Dec 17 2014

Extensions

a(12) from Chai Wah Wu, Dec 17 2014
a(13)-a(14) from Giovanni Resta, Apr 20 2016
a(15) from Bert Dobbelaere, Mar 04 2019
a(16)-a(17) from Bert Dobbelaere, Mar 20 2019

A215728 a(n) is the smallest m for which 5^m contains n consecutive identical digits.

Original entry on oeis.org

0, 11, 50, 95, 125, 1087, 2786, 2790, 2796, 2797, 2802, 2803, 1040703, 5547565, 7761841, 17876345
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Comments

a(13) > 893000. - Chai Wah Wu, Dec 17 2014

Crossrefs

Programs

  • Python
    def A215728(n):
        l, x = [str(d)*n for d in range(10)], 1
        for m in range(10**9):
            s = str(x)
            for k in l:
                if k in s:
                    return m
            x *= 5
        return 'search limit reached'
    # Chai Wah Wu, Dec 17 2014

Extensions

a(13)-a(14) from Giovanni Resta, Apr 19 2016
a(15)-a(16) from Bert Dobbelaere, Feb 13 2019

A215729 a(n) is the smallest m for which 6^m contains (at least) n consecutive identical digits.

Original entry on oeis.org

0, 5, 5, 115, 226, 371, 1503, 8533, 27717, 27717, 69936, 848255, 1308931, 8255246, 32564822, 39063403
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Comments

a(12) > 838000. - Chai Wah Wu, Dec 17 2014
a(14) > 7*10^6. - Giovanni Resta, Apr 20 2016

Crossrefs

Programs

  • Python
    def A215729(n):
        l, x = [str(d)*n for d in range(10)], 1
        for m in range(10**9):
            s = str(x)
            for k in l:
                if k in s:
                    return m
            x *= 6
        return 'search limit reached'
    # Chai Wah Wu, Dec 17 2014

Extensions

a(11) from Rick van der Hoorn, Mar 26 2013
a(12)-a(13) from Giovanni Resta, Apr 19 2016
a(14) from Bert Dobbelaere, Feb 15 2019
a(15) from Paul Geneau de Lamarlière, May 26 2024
a(16) from Paul Geneau de Lamarlière, Jul 12 2024

A215730 a(n) is the smallest m for which 7^m contains n consecutive identical digits.

Original entry on oeis.org

0, 6, 31, 71, 172, 175, 1961, 6176, 33836, 61282, 305871, 856635, 2135396, 7291510, 11032874, 30775389
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Comments

a(13) > 1116000. - Chai Wah Wu, Dec 17 2014
a(14) > 7*10^6. - Giovanni Resta, Apr 20 2016

Examples

			7^31 = 157775382034845806615042743 contains 3 consecutive identical digits.
		

Crossrefs

Programs

  • Python
    import sys
    sys.set_int_max_str_digits(200000)
    def a(n):
      st = "0123456789"
      for k in range(10**6):
        s = str(7**k)
        tot = 0
        for i in st:
          if s.count(i*n) > 0:
            tot += 1
            break
        if tot > 0:
          return k
    n = 1
    while n < 10:
      print(a(n), end=', ')
      n += 1
    # Derek Orr, Jul 28 2014
    
  • Python
    def A215730(n):
        l, x = [str(d)*n for d in range(10)], 1
        for m in range(10**9):
            s = str(x)
            for k in l:
                if k in s:
                    return m
            x *= 7
        return 'search limit reached'
    # Chai Wah Wu, Dec 17 2014

Extensions

Added a(10), Rick van der Hoorn, Mar 26 2013
a(11)-a(12) from Hiroaki Yamanouchi, Aug 29 2014
a(13) from Giovanni Resta, Apr 19 2016
a(14)-a(15) from Bert Dobbelaere, Feb 15 2019
a(16) from Paul Geneau de Lamarlière, Jul 16 2024

A215733 a(n) is the first digit to appear n times in succession in a power of 3.

Original entry on oeis.org

1, 7, 8, 5, 5, 8, 2, 1, 2, 2, 2, 4, 5, 8, 2, 4, 4
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Crossrefs

Programs

  • Python
    def A215733(n):
        l, x = [str(d)*n for d in range(10)], 1
        for m in range(10**9):
            s = str(x)
            for k in range(10):
                if l[k] in s:
                    return k
            x *= 3
        return 'search limit reached'
    # Chai Wah Wu, Dec 17 2014

Extensions

a(12) from Chai Wah Wu, Dec 17 2014
a(13)-a(14) from Giovanni Resta, Apr 20 2016
a(15) from Bert Dobbelaere, Mar 04 2019
a(16)-a(17) from Bert Dobbelaere, Mar 20 2019

A215731 a(n) is the smallest m for which the decimal representation of 11^m contains n consecutive identical digits.

Original entry on oeis.org

0, 1, 8, 39, 156, 482, 1323, 2983, 9443, 39879, 214747, 296095, 296095, 5541239, 8621384, 30789328
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Examples

			The decimal representation of 11^39879 contains ten consecutive 6s, and is the least such power with such a string of digits.
		

Crossrefs

Cf. A215737 (the repeated digits), A045875, A215727, A215728, A215729, A215730.

Programs

  • Mathematica
    mostDigits[t_] := Module[{lastDigit = t[[1]], record = 1, cnt = 1}, Do[If[t[[n]] == lastDigit, cnt++, If[cnt > record, record = cnt]; cnt = 1; lastDigit = t[[n]]], {n, 2, Length[t]}]; If[cnt > record, record = cnt] ; record]; nn = 10; t = Table[-1, {nn}]; n = -1; While[Min[t] == -1, n++; c = mostDigits[IntegerDigits[11^n]]; If[c > nn, c = nn]; While[c > 0 && t[[c]] == -1, t[[c]] = n; c--]]; t (* T. D. Noe, Apr 29 2013 *)
  • Python
    def A215731(n):
        l, x = [str(d)*n for d in range(10)], 1
        for m in range(10**9):
            s = str(x)
            for k in l:
                if k in s:
                    return m
            x *= 11
        return 'search limit reached'
    # Chai Wah Wu, Dec 17 2014

Extensions

a(10) discovered by "Wick" (See http://www.mersenneforum.org/showpost.php?p=334789&postcount=89). Definition clarified and all terms to a(10) verified by Daran Gill, Mar 24 2013
a(11) discovered by Tom Womack (See http://www.mersenneforum.org/showpost.php?p=337916&postcount=105), Rick van der Hoorn, Apr 24 2013
a(12)-a(13) from Giovanni Resta, Apr 25 2013
Corrected a(12), Rick van der Hoorn, Apr 28 2013
a(14) from Giovanni Resta, Apr 18 2016
a(15) from Bert Dobbelaere, Feb 15 2019
a(16) from Paul Geneau de Lamarlière, Oct 03 2024

A215734 a(n) is the first digit to appear n times in succession in a power of 5.

Original entry on oeis.org

1, 8, 8, 7, 4, 2, 8, 5, 5, 7, 5, 7, 4, 1, 5, 7
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Crossrefs

Extensions

a(13)-a(14) from Giovanni Resta, Apr 19 2016
a(15)-a(16) from Bert Dobbelaere, Feb 13 2019

A215735 a(n) is the first digit to appear n times in succession in a power of 6.

Original entry on oeis.org

1, 7, 7, 0, 2, 1, 2, 7, 1, 1, 0, 5, 7, 6, 3, 7
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Crossrefs

See A215729 for the powers.

Extensions

a(11) added by V. Raman, Nov 23 2013
a(12)-a(13) from Giovanni Resta, Apr 19 2016
a(14) from Bert Dobbelaere, Feb 15 2019
a(15) from Paul Geneau de Lamarlière, Jun 26 2024
a(16) from Paul Geneau de Lamarlière, Jul 12 2024

A215737 a(n) is the first digit to appear n times in succession in a power of 11.

Original entry on oeis.org

1, 1, 8, 7, 6, 0, 6, 0, 9, 6, 6, 2, 2, 7, 6, 9
Offset: 1

Views

Author

V. Raman, Aug 22 2012

Keywords

Crossrefs

Cf. A001020 (powers of 11), A045875, A215731, A215732.

Programs

  • Mathematica
    n = 1; x = 1; lst = {};
    For[i = 1, i <= 10000, i++,
    z = Split[IntegerDigits[x]]; a = Length /@ z; b = Max[a];
    For[j = n, j <= b, j++,
      AppendTo[lst, First[First[Part[z, First[Position[a, b]]]]]]; n++
    ]; x = 11 x ]; lst  (* Robert Price, Mar 16 2019 *)
  • Python
    def A215737(n):
        a, s = 1, tuple(str(i)*n for i in range(10))
        while True:
            a *= 11
            t = str(a)
            for i, x in enumerate(s):
                if x in t:
                    return i # Chai Wah Wu, Mar 30 2021

Extensions

a(10)-a(13) added by V. Raman, Apr 30 2012, in correspondence with A215731.
a(14) from Giovanni Resta, Apr 18 2016
a(15) from Bert Dobbelaere, Feb 15 2019
a(16) from Paul Geneau de Lamarlière, Oct 03 2024
Showing 1-10 of 25 results. Next