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.

Previous Showing 21-26 of 26 results.

A131540 Exponent of least power of 2 having exactly n consecutive 6's in its decimal representation.

Original entry on oeis.org

0, 4, 46, 157, 222, 220, 2269, 11019, 18842, 192918, 192916, 271979, 1039316, 7193133, 14060686, 97428976
Offset: 0

Views

Author

Shyam Sunder Gupta, Aug 26 2007

Keywords

Examples

			a(3)=157 because 2^157(i.e. 182687704666362864775460604089535377456991567872) is the smallest power of 2 to contain a run of 3 consecutive sixes in its decimal form.

Links

  • Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC9-16.

Crossrefs

Cf. A006889, A131535, A131536, A131537, A131538, A131539, A131541, A131542, A131543.

Programs

  • Mathematica
    a = ""; Do[ a = StringJoin[a, "6"]; b = StringJoin[a, "6"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

Extensions

Two more terms from Sean A. Irvine, May 31 2010
a(13)-a(14) from Lars Blomberg, Jan 24 2013
a(15) from Bert Dobbelaere, Mar 07 2019
a(0)=0 prepended by Paul Geneau de Lamarlière, Jul 20 2024

A131541 Exponent of least power of 2 having exactly n consecutive 7's in its decimal representation.

Original entry on oeis.org

0, 15, 27, 24, 181, 317, 2309, 972, 25264, 131979, 279275, 279269, 1727605, 6030752, 8760853, 77235364
Offset: 0

Views

Author

Shyam Sunder Gupta, Aug 26 2007

Keywords

Examples

			a(3)=24 because 2^24(i.e. 16777216) is the smallest power of 2 to contain a run of 3 consecutive sevens in its decimal form.

Links

  • Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC9-16.

Crossrefs

Cf. A006889, A131535, A131536, A131537, A131538, A131539, A131540, A131542, A131543.

Programs

  • Mathematica
    a = ""; Do[ a = StringJoin[a, "7"]; b = StringJoin[a, "7"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

Extensions

a(11)-a(12) from Sean A. Irvine, May 31 2010
a(13)-a(14) from Lars Blomberg, Jan 24 2013
a(15) from Bert Dobbelaere, Mar 02 2019
a(0)=0 prepended by Paul Geneau de Lamarlière, Jul 20 2024

A259082 a(n) = largest k such that the decimal representation of 5^k does not contain the digit n, or -1 if every power of 5 contains the digit n.

Original entry on oeis.org

58, 42, 1, 23, 55, -1, 45, 53, 24, 65
Offset: 0

Views

Author

N. J. A. Sloane, Jun 18 2015

Keywords

Comments

These values are only conjectural.

Links

  • Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC9-16.

A259084 a(n) = largest k such that the decimal representation of prime(n)^k does not contain the digit 0.

Original entry on oeis.org

86, 68, 58, 35, 41, 14, 27, 44, 10, 14, 16, 16, 9, 10, 8, 7, 14, 16, 14, 8, 6, 9, 4, 23, 8, 0, 14, 10, 12, 10, 6, 14, 5, 8, 5, 13, 7, 16, 7, 17, 6, 3, 9, 9, 16, 7, 12, 11, 4, 13, 7, 16, 8, 9, 3, 10, 4, 9, 6, 4, 5, 13, 3, 12, 7, 9, 6, 8, 4, 39, 13, 12, 10, 4
Offset: 1

Views

Author

N. J. A. Sloane, Jun 18 2015

Keywords

Comments

These values are only conjectural.
a(n) = 0 if prime(n) is in A062800. - Robert Israel, Jun 19 2015

Examples

			a(1)=86 because 2^86 = 77371252455336267181195264 is conjectured to be the highest power of 2 that doesn't contain the digit 0.

Links

Crossrefs

Cf. A062800, A094776, A259081-A259086.

Programs

  • Maple
    N:= 100: K:= 100:  # to get a(1) to a(N), searching up to k = K
for n from 1 to N do
  p:= ithprime(n);
  A[n]:= 0;
  for k from 1 to K do
    if not has(convert(p^k,base,10),0) then
       A[n]:= k
    fi
  od
od:
seq(A[n],n=1..N); # Robert Israel, Jun 19 2015

Extensions

a(14)-a(57) from Hiroaki Yamanouchi, Jun 19 2015

A360623 Largest k such that the decimal representation of 2^k is missing any n-digit string.

Original entry on oeis.org

168, 3499, 53992, 653060
Offset: 1

Views

Author

Hans Havermann, Feb 14 2023

Keywords

Comments

All terms are conjectural, checked up to 10^6.

Examples

			168 is the largest base-ten power of 2 that is missing any of the 10 length-1 digit-strings (missing '2').
3499 is the largest base-ten power of 2 that is missing any of the 100 length-2 digit-strings (missing '95').
53992 is the largest base-ten power of 2 that is missing any of the 1000 length-3 digit-strings (missing '661').
653060 is the largest base-ten power of 2 that is missing any of the 10000 length-4 digit-strings (missing '6164').

Links

Crossrefs

Cf. A094776, A360656.

A372680 Integers k such that 2^k contains all powers of 2 not exceeding k as substrings.

Original entry on oeis.org

124, 192, 322, 808, 830, 957, 1757, 4067, 5489, 6616, 6724, 6794, 7065, 7727, 7728, 7736, 8253, 8938, 9438, 9989, 10194, 10195, 10271, 10350, 10389, 10397, 10445, 10475, 10611, 10835, 11107, 11500, 11606, 11758, 11835, 12089, 12304, 12398, 12501, 12548, 12645, 12694, 12695, 12734, 12820
Offset: 1

Views

Author

Bryle Morga, May 10 2024

Keywords

Comments

It is unknown whether this sequence contains infinitely many terms.

Examples

			124 is a term; 2^124 = 21267647932558653966460912964485513216 contains 2, 4, 8, 16, 32, 64 as substrings.

Crossrefs

Cf. A046300, A094776, A371808.

Programs

  • Python
    def f(m):
  a = str(2**m)
  for i in range(0, m.bit_length()):
    if str(2**i) not in a:
      return 0
  return 1
def a(n):
  m = 0
  i = 0
  while i != n:
    m += 1
    i += f(m)
  return m
Previous Showing 21-26 of 26 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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