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.

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A154462 Decimal expansion of log_2 (14).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			3.8073549220576041074419693172318308086410266259661407836772...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), this sequence, A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2,14],10,120][[1]] (* Harvey P. Dale, Jul 19 2013 *)

Formula

Equals 1+A020860. - R. J. Mathar, Feb 01 2023

A154540 Decimal expansion of log_2 (15).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			3.9068905956085185293240583734372066846246458007170616725105...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), this sequence, A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 15], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A154905 Decimal expansion of log_2 (18).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.1699250014423123629074778878956330175196288153849621209115...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), this sequence, A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2,18],10,120][[1]] (* Harvey P. Dale, Jul 12 2012 *)

Formula

Equals 1 + A020861 = 1 + 2*A020857. - Jianing Song, Nov 16 2024

A154995 Decimal expansion of log_2 (19).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.2479275134435854937935194229068344226935075696615340145815...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), this sequence, A155172 (m=20), A155536 (m=21), A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 19], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A155536 Decimal expansion of log_2 (21).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.3923174227787602888957082611796473174008410336586218441330...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), this sequence, A155693 (m=22), A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 21], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A155693 Decimal expansion of log_2 (22).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.4594316186372972561993630467257929587032315256817680713128...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), this sequence, A155793 (m=23), A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 22], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

Formula

Equals 1 + A020863. - Jianing Song, Nov 16 2024

A155793 Decimal expansion of log_2 (23).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			4.5235619560570128722941482441626688444988251254425550594944...

Links

Crossrefs

Cf. decimal expansion of log_2(m): A020857 (m=3), A020858 (m=5), A020859 (m=6), A020860 (m=7), A020861 (m=9), A020862 (m=10), A020863 (m=11), A020864 (m=12), A152590 (m=13), A154462 (m=14), A154540 (m=15), A154847 (m=17), A154905 (m=18), A154995 (m=19), A155172 (m=20), A155536 (m=21), A155693 (m=22), this sequence, A155921 (m=24).

Programs

  • Mathematica
    RealDigits[Log[2, 23], 10, 100][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

A008559 a(1)=2; thereafter, convert a(n-1) from base 10 to base 2 but regard the result as a base 10 number.

Original entry on oeis.org

2, 10, 1010, 1111110010, 1000010001110100011000101111010
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

The previous number is converted to binary digits and then the digits are regarded as decimal digits in the next number in the sequence. - Michael Somos, May 16 2014
The next term has 100 digits. - Harvey P. Dale, Jul 16 2011
The number of decimal digits of a(n) is A242347(n). - Robert G. Wilson v, Jul 10 2013
log(a(n))/log(a(n-1)) ~ log_2(10) = A020862. - Robert G. Wilson v, Jul 10 2013

References

  • Clifford Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 350.

Links

Crossrefs

Cf. A006937 (essentially the same sequence).
For initial terms 2 through 12 see A008559, A006938, A260025, A260024, A260026, A260027, A260028, A260029, A008559 (again), A006938 (again), A260030 respectively.

Programs

  • Maple
    f:=proc(n) local i,j,r; i:=convert(n,base,2); j:=add(i[r]*10^(r-1),r=1..nops(i)); end;
g:=proc(n,M) global f; local a,b,t1; a:=n; t1:=[a]; for i from 1 to M do b:=f(a); t1:=[op(t1),b]; a:=b; od; t1; end; g(2,5); # N. J. A. Sloane, Jul 14 2015
  • Mathematica
    NestList[FromDigits[IntegerDigits[#,2]]&,2,5] (* Harvey P. Dale, Jul 16 2011 *)
  • PARI
    lista(nn) = my(k=2); print1(k); for(n=2, nn, print1(", ", k=fromdigits(binary(k)))); \\ Jinyuan Wang, Jan 18 2025
  • Python
    A008559_list = [2]
for _ in range(5):
    A008559_list.append(int(bin(A008559_list[-1])[2:]))
# Chai Wah Wu, Dec 26 2014

Extensions

Comment corrected by Chai Wah Wu, Dec 26 2014

A006938 Convert the last term from decimal to binary! a(1)=3.

Original entry on oeis.org

3, 11, 1011, 1111110011, 1000010001110100011000101111011
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

The next term (a(6)) has 100 digits. - Harvey P. Dale, Feb 28 2012
The number of digits of a(n) are 1, 2, 4, 10, 31, 100, 330, 1093, 3628, 12049, 40023, 132951, 441651, 1467130, 4873698, 16190071, 53782249, 178660761, ... - Robert G. Wilson v, Jul 10 2013
log(a(n))/log(a(n-1)) ~ log_2(10) = A020862. - Robert G. Wilson v, Jul 10 2013

References

  • C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 350.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

For initial terms 2 through 12 see A008559, A006938, A260025, A260024, A260026, A260027, A260028, A260029, A008559 (again), A006938 (again), A260030 respectively.

Programs

  • Mathematica
    NestList[FromDigits[IntegerDigits[#,2]]&,3,4] (* Harvey P. Dale, Feb 28 2012 *)
  • PARI
    lista(nn) = my(k=3); print1(k); for(n=2, nn, print1(", ", k=fromdigits(binary(k)))); \\ Jinyuan Wang, Jan 18 2025
  • Python
    def agen(an):
  while True: yield an; an = int(bin(an)[2:])
g = agen(3)
print([next(g) for i in range(5)]) # Michael S. Branicky, Mar 11 2021

Extensions

a(1)=3 added by N. J. A. Sloane, Jul 14 2015

A066343 Beatty sequence for log_2(10).

Original entry on oeis.org

3, 6, 9, 13, 16, 19, 23, 26, 29, 33, 36, 39, 43, 46, 49, 53, 56, 59, 63, 66, 69, 73, 76, 79, 83, 86, 89, 93, 96, 99, 102, 106, 109, 112, 116, 119, 122, 126, 129, 132, 136, 139, 142, 146, 149, 152, 156, 159, 162, 166, 169, 172, 176, 179, 182, 186, 189, 192, 195, 199
Offset: 1

Views

Author

Vladeta Jovovic, Dec 15 2001

Keywords

Comments

Number of positive integers <= 10^n that are divisible by no prime exceeding 2.
Maximum number of prime divisors of positive integers <= 10^n counted with multiplicity. - Martin Renner, Apr 04 2014
You wish to represent the rational number n/d in decimal notation, where n is an integer, d is a nonzero integer, and precision(d) represents the number of decimal digits in d. The decimal notation representation of n/d will either terminate or repeat with a repetend. If the decimal notation representation terminates then this sequence defines the maximum number of decimal digits to the right of the decimal point (after truncating trailing zeros) for a given precision of d ... floor(precision(d) * log_2(10)). - Michael T Howard, Jul 17 2017
Beatty complement of A066344. - Jianing Song, Jan 27 2019

Links

Crossrefs

Cf. A066344, A067497, A129344.
Cf. A020862 (log_2(10)).

Programs

  • Maple
    seq(floor(log[2](10)*n),n=1..60); # Martin Renner, Apr 04 2014
  • Mathematica
    Table[ Floor[ n*Log[2, 10]], {n, 60}] (* Robert G. Wilson v, May 27 2005 *)
  • PARI
    { l=log(10)/log(2); for (n=1, 1000, a=floor(n*l); write("b066343.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 11 2010
  • Python
    def A066343(n): return (5**n).bit_length()+n-1 # Chai Wah Wu, Sep 08 2024

Formula

a(n) = floor(n*log_2(10)).
Previous Showing 11-20 of 26 results. Next

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