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 11-19 of 19 results.

A154849 Decimal expansion of log_4 (17).

Original entry on oeis.org

2, 0, 4, 3, 7, 3, 1, 4, 2, 0, 6, 2, 5, 1, 6, 9, 7, 0, 4, 1, 2, 7, 0, 3, 3, 0, 0, 5, 4, 0, 5, 2, 0, 2, 1, 7, 7, 0, 0, 5, 6, 3, 3, 6, 4, 1, 1, 7, 2, 4, 1, 0, 3, 4, 4, 0, 6, 3, 3, 0, 4, 5, 3, 2, 1, 9, 3, 3, 4, 8, 2, 5, 4, 5, 2, 3, 6, 9, 1, 0, 3, 4, 1, 4, 8, 6, 7, 1, 5, 7, 5, 9, 2, 1, 8, 4, 2, 1, 3
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			2.0437314206251697041270330054052021770056336411724103440633...

Links

Crossrefs

Cf. decimal expansion of log_4(m): A094148 (m=3), A153201 (m=5), A153460 (m=6), A153615 (m=7), A154155 (m=10), A154176 (m=11), A154197 (m=12), A154224 (m=13), A154464 (m=14), A154543 (m=15), this sequence, A154909 (m=18), A155004 (m=19), A155183 (m=20), A155545 (m=21), A155695 (m=22), A155818 (m=23), A155936 (m=24).

Programs

  • Mathematica
    RealDigits[Log[4, 17], 10, 100][[1]] (* Vincenzo Librandi, Aug 30 2013 *)

A154909 Decimal expansion of log_4 (18).

Original entry on oeis.org

2, 0, 8, 4, 9, 6, 2, 5, 0, 0, 7, 2, 1, 1, 5, 6, 1, 8, 1, 4, 5, 3, 7, 3, 8, 9, 4, 3, 9, 4, 7, 8, 1, 6, 5, 0, 8, 7, 5, 9, 8, 1, 4, 4, 0, 7, 6, 9, 2, 4, 8, 1, 0, 6, 0, 4, 5, 5, 7, 5, 2, 6, 5, 4, 5, 4, 1, 0, 9, 8, 2, 2, 7, 7, 9, 4, 3, 5, 8, 5, 6, 2, 5, 2, 2, 2, 8, 0, 4, 7, 4, 9, 1, 8, 0, 8, 8, 2, 4
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			2.0849625007211561814537389439478165087598144076924810604557...

Links

Crossrefs

Cf. A020857 (log_2(3)).
Cf. decimal expansion of log_4(m): A094148 (m=3), A153201 (m=5), A153460 (m=6), A153615 (m=7), A154155 (m=10), A154176 (m=11), A154197 (m=12), A154224 (m=13), A154464 (m=14), A154543 (m=15), A154849 (m=17), this sequence, A155004 (m=19), A155183 (m=20), A155545 (m=21), A155695 (m=22), A155818 (m=23), A155936 (m=24).

Programs

  • Mathematica
    RealDigits[Log[4, 18], 10, 100][[1]] (* Vincenzo Librandi, Aug 30 2013 *)

Formula

Equals A020857+1/2. - R. J. Mathar, Feb 15 2025

A155004 Decimal expansion of log_4 (19).

Original entry on oeis.org

2, 1, 2, 3, 9, 6, 3, 7, 5, 6, 7, 2, 1, 7, 9, 2, 7, 4, 6, 8, 9, 6, 7, 5, 9, 7, 1, 1, 4, 5, 3, 4, 1, 7, 2, 1, 1, 3, 4, 6, 7, 5, 3, 7, 8, 4, 8, 3, 0, 7, 6, 7, 0, 0, 7, 2, 9, 0, 7, 6, 2, 3, 6, 5, 4, 3, 2, 2, 8, 2, 6, 0, 4, 1, 0, 2, 7, 3, 2, 4, 4, 3, 4, 0, 1, 3, 5, 4, 0, 2, 7, 0, 8, 6, 0, 8, 8, 2, 5
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			2.1239637567217927468967597114534172113467537848307670072907...

Links

Crossrefs

Cf. decimal expansion of log_4(m): A094148 (m=3), A153201 (m=5), A153460 (m=6), A153615 (m=7), A154155 (m=10), A154176 (m=11), A154197 (m=12), A154224 (m=13), A154464 (m=14), A154543 (m=15), A154849 (m=17), A154909 (m=18), this sequence, A155183 (m=20), A155545 (m=21), A155695 (m=22), A155818 (m=23), A155936 (m=24).
Cf. A016627, A016642.

Programs

A155183 Decimal expansion of log_4 (20).

Original entry on oeis.org

2, 1, 6, 0, 9, 6, 4, 0, 4, 7, 4, 4, 3, 6, 8, 1, 1, 7, 3, 9, 3, 5, 1, 5, 9, 7, 1, 4, 7, 4, 4, 6, 9, 5, 0, 8, 7, 9, 3, 2, 4, 1, 5, 6, 9, 6, 5, 1, 2, 2, 9, 0, 3, 0, 6, 0, 2, 7, 3, 7, 8, 1, 9, 7, 9, 0, 7, 9, 6, 7, 3, 8, 8, 3, 0, 4, 3, 1, 2, 6, 0, 7, 9, 2, 5, 0, 6, 9, 8, 7, 1, 6, 7, 9, 6, 8, 5, 0, 7
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			2.1609640474436811739351597147446950879324156965122903060273...

Links

Crossrefs

Cf. decimal expansion of log_4(m): A094148 (m=3), A153201 (m=5), A153460 (m=6), A153615 (m=7), A154155 (m=10), A154176 (m=11), A154197 (m=12), A154224 (m=13), A154464 (m=14), A154543 (m=15), A154849 (m=17), A154909 (m=18), A155004 (m=19), this sequence, A155545 (m=21), A155695 (m=22), A155818 (m=23), A155936 (m=24).

Programs

  • Mathematica
    RealDigits[Log[4, 20], 10, 100][[1]] (* Vincenzo Librandi, Aug 30 2013 *)

Formula

Equals 1/2+ A154155 = 1 + A153201. - R. J. Mathar, May 25 2023

A155545 Decimal expansion of log_4 (21).

Original entry on oeis.org

2, 1, 9, 6, 1, 5, 8, 7, 1, 1, 3, 8, 9, 3, 8, 0, 1, 4, 4, 4, 4, 7, 8, 5, 4, 1, 3, 0, 5, 8, 9, 8, 2, 3, 6, 5, 8, 7, 0, 0, 4, 2, 0, 5, 1, 6, 8, 2, 9, 3, 1, 0, 9, 2, 2, 0, 6, 6, 5, 2, 2, 1, 8, 9, 3, 0, 5, 7, 0, 9, 5, 3, 8, 3, 2, 8, 2, 7, 5, 7, 7, 4, 5, 1, 0, 0, 7, 0, 7, 3, 7, 0, 4, 4, 1, 4, 9, 5, 1
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			2.1961587113893801444478541305898236587004205168293109220665...

Links

Crossrefs

Cf. decimal expansion of log_4(m): A094148 (m=3), A153201 (m=5), A153460 (m=6), A153615 (m=7), A154155 (m=10), A154176 (m=11), A154197 (m=12), A154224 (m=13), A154464 (m=14), A154543 (m=15), A154849 (m=17), A154909 (m=18), A155004 (m=19), A155183 (m=20), this sequence, A155695 (m=22), A155818 (m=23), A155936 (m=24).

Programs

  • Mathematica
    RealDigits[Log[4, 21], 10, 100][[1]] (* Vincenzo Librandi, Aug 30 2013 *)

A155695 Decimal expansion of log_4 (22).

Original entry on oeis.org

2, 2, 2, 9, 7, 1, 5, 8, 0, 9, 3, 1, 8, 6, 4, 8, 6, 2, 8, 0, 9, 9, 6, 8, 1, 5, 2, 3, 3, 6, 2, 8, 9, 6, 4, 7, 9, 3, 5, 1, 6, 1, 5, 7, 6, 2, 8, 4, 0, 8, 8, 4, 0, 3, 5, 6, 5, 6, 4, 0, 0, 8, 2, 2, 8, 6, 3, 1, 6, 5, 3, 0, 9, 8, 6, 0, 0, 0, 9, 1, 7, 6, 3, 5, 4, 7, 4, 5, 6, 4, 9, 6, 4, 3, 4, 5, 0, 2, 4
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			2.2297158093186486280996815233628964793516157628408840356564...

Links

Crossrefs

Cf. decimal expansion of log_4(m): A094148 (m=3), A153201 (m=5), A153460 (m=6), A153615 (m=7), A154155 (m=10), A154176 (m=11), A154197 (m=12), A154224 (m=13), A154464 (m=14), A154543 (m=15), A154849 (m=17), A154909 (m=18), A155004 (m=19), A155183 (m=20), A155545 (m=21), this sequence, A155818 (m=23), A155936 (m=24).

Programs

  • Mathematica
    RealDigits[Log[4,22],10,100][[1]]  (* Harvey P. Dale, Apr 18 2011 *)

A155818 Decimal expansion of log_4 (23).

Original entry on oeis.org

2, 2, 6, 1, 7, 8, 0, 9, 7, 8, 0, 2, 8, 5, 0, 6, 4, 3, 6, 1, 4, 7, 0, 7, 4, 1, 2, 2, 0, 8, 1, 3, 3, 4, 4, 2, 2, 2, 4, 9, 4, 1, 2, 5, 6, 2, 7, 2, 1, 2, 7, 7, 5, 2, 9, 7, 4, 7, 2, 2, 1, 8, 6, 6, 0, 0, 7, 3, 8, 9, 0, 7, 2, 7, 8, 1, 3, 8, 2, 3, 4, 8, 0, 5, 5, 3, 7, 7, 2, 6, 2, 9, 3, 1, 0, 4, 4, 1, 0
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			2.2617809780285064361470741220813344222494125627212775297472...

Links

Crossrefs

Cf. decimal expansion of log_4(m): A094148 (m=3), A153201 (m=5), A153460 (m=6), A153615 (m=7), A154155 (m=10), A154176 (m=11), A154197 (m=12), A154224 (m=13), A154464 (m=14), A154543 (m=15), A154849 (m=17), A154909 (m=18), A155004 (m=19), A155183 (m=20), A155545 (m=21), A155695 (m=22), this sequence, A155936 (m=24).

Programs

  • Mathematica
    RealDigits[Log[4, 23], 10, 100][[1]] (* Vincenzo Librandi, Aug 30 2013 *)

A155936 Decimal expansion of log_4 (24).

Original entry on oeis.org

2, 2, 9, 2, 4, 8, 1, 2, 5, 0, 3, 6, 0, 5, 7, 8, 0, 9, 0, 7, 2, 6, 8, 6, 9, 4, 7, 1, 9, 7, 3, 9, 0, 8, 2, 5, 4, 3, 7, 9, 9, 0, 7, 2, 0, 3, 8, 4, 6, 2, 4, 0, 5, 3, 0, 2, 2, 7, 8, 7, 6, 3, 2, 7, 2, 7, 0, 5, 4, 9, 1, 1, 3, 8, 9, 7, 1, 7, 9, 2, 8, 1, 2, 6, 1, 1, 4, 0, 2, 3, 7, 4, 5, 9, 0, 4, 4, 1, 2
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			2.2924812503605780907268694719739082543799072038462405302278...

Links

Crossrefs

Cf. decimal expansion of log_4(m): A094148 (m=3), A153201 (m=5), A153460 (m=6), A153615 (m=7), A154155 (m=10), A154176 (m=11), A154197 (m=12), A154224 (m=13), A154464 (m=14), A154543 (m=15), A154849 (m=17), A154909 (m=18), A155004 (m=19), A155183 (m=20), A155545 (m=21), A155695 (m=22), A155818 (m=23), this sequence.

Programs

  • Mathematica
    RealDigits[Log[4, 24], 10, 100][[1]] (* Vincenzo Librandi, Aug 30 2013 *)

Formula

3/2 + A094148. - R. J. Mathar, Sep 24 2011

A378048 Numbers k such that k and k^2 together use at most 4 distinct decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 35, 38, 40, 41, 45, 46, 50, 55, 56, 60, 63, 64, 65, 66, 68, 70, 74, 75, 76, 77, 80, 81, 83, 85, 88, 90, 91, 95, 96, 97, 99, 100, 101, 102, 105, 109, 110
Offset: 1

Views

Author

Jovan Radenkovicc, Nov 15 2024

Keywords

Comments

Problem: Is there a real constant c such that a(n) < n^c for all positive integers n?
All of A136808, A136809, A136816, ..., A137079 are subsequences. Many if not most terms of A058411, A058413, ... ("tridigital solutions") are also in this sequence; see also Hisanori Mishima's web page for some nontrivial solutions. - M. F. Hasler, Feb 02 2025

Examples

			816 is in the sequence since 816^2 = 665856 and both together use at most 4 distinct digits.
149 is not in the sequence since 149^2 = 22201 and both together use 5 distinct digits.

Links

Crossrefs

Supersequence of A136808, A136809, A136816, A136822.
Cf. A043537, A053061, A055436, A154155.

Programs

  • Magma
    [n: n in [0..1000000] | #Set(Intseq(n)) le 4 and #Set(Intseq(n) cat Intseq(n^2)) le 4];
  • Mathematica
    Select[Range[0, 110], Length[Union @@ IntegerDigits@ {#, #^2}] < 5 &] (* Amiram Eldar, Nov 15 2024 *)
  • PARI
    isok(k) = #Set(concat(digits(k), digits(k^2))) <= 4; \\ Michel Marcus, Nov 15 2024
  • PARI
    is(n)=my(s=Set(digits(n))); #s<5 && #setunion(Set(digits(n^2)),s)<5 \\ Charles R Greathouse IV, Jan 30 2025
  • PARI
    is1(n)=#setunion(Set(digits(n^2)),Set(digits(n)))<5
ok(m)=my(d=concat(apply(k->digits(lift(k)), [m,m^2]))
test(d)=my(v=List(),D=10^d); for(n=0,D-1, if(ok(Mod(n,D)), listput(v,n))); Vec(v)
res=test(8); \\ build a list of residues mod 10^8
D=diff(concat(res,res[1]+10^8)); #D
u=List(); for(n=0,10^7, if(is1(n) && !setsearch(n,res), listput(u,n))); \\ build exceptions
setminus(select(is1,[0..n]),list(n))
list(lim)=my(v=List(u)); forstep(n=0,lim,D, if(is1(n), listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Jan 30 2025
  • Python
    def ok(n): return len(set(str(n)+str(n**2))) <= 4
print([k for k in range(111) if ok(k)]) # Michael S. Branicky, Nov 18 2024

Formula

A043537(A053061(a(n))) <= 4.
Trivially, a(n) >> n^1.66... where the exponent is log(10)/log(4) (A154155). - Charles R Greathouse IV, Jan 30 2025
Previous Showing 11-19 of 19 results.

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

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