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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A153498 Palindromes formed from concatenation of A147759(n) and the same string A147759(n) but without its initial digit.

Original entry on oeis.org

1, 111, 10101, 1001001, 101010101, 10110101101, 1010101010101, 101001010100101, 10101010101010101, 1010110101010110101, 101010101010101010101, 10101001010101010010101
Offset: 1

Views

Author

Omar E. Pol, Dec 27 2008, Feb 18 2009

Keywords

Comments

a(n) is also A153497(n) written in base 2.

Examples

			n ............. a(n)
1 .............. 1
2 ............. 111
3 ............ 10101
4 ........... 1001001
5 .......... 101010101
6 ......... 10110101101
7 ........ 1010101010101
8 ....... 101001010100101
9 ...... 10101010101010101
10 .... 1010110101010110101
11 ... 101010101010101010101
======================================
Another visualization of the structure
======================================
1 .............. *
2 ............. /|\
3 ............ /.|.\
4 ........... /..|..\
5 .......... /.*.|.*.\
6 ......... /./|.|.|\.\
7 ........ /./.|.|.|.\.\
8 ....... /./..|.|.|..\.\
9 ...... /./.*.|.|.|.*.\.\
10 .... /././|.|.|.|.|\.\.\
11 ... /././.|.|.|.|.|.\.\.\

Links

Crossrefs

Cf. A135577, A138146, A152576, A152764, A153497, A153499, A153500, A144564.

Formula

From R. J. Mathar, Feb 20 2009: (Start)
a(n)=101*a(n-1)-1110*a(n-2)+102010*a(n-3)-111000*a(n-4)+1010000*a(n-5)-1000000*a(n-6).
G.f.: x(1+10x+2000x^3-91000*x^4+100000x^5)/((1-100x)(1-x)(1+10x^2)(1+1000x^2)). (End)

Extensions

More terms from R. J. Mathar, Feb 20 2009
Keyword:base added by Charles R Greathouse IV, Apr 23 2010

A144564 Bisection of A147757.

Original entry on oeis.org

1, 101, 10101, 1011101, 101111101, 10111111101, 1011111111101, 101111111111101, 10111111111111101, 1011111111111111101, 101111111111111111101, 10111111111111111111101, 1011111111111111111111101, 101111111111111111111111101, 10111111111111111111111111101
Offset: 1

Views

Author

Omar E. Pol, Dec 14 2008

Keywords

Examples

			n ...... a(n)
1 ....... 1
2 ...... 101
3 ..... 10101
4 .... 1011101
5 ... 101111101

Links

Crossrefs

Cf. A135577, A138120, A138146, A147757, A152756.

Programs

  • Mathematica
    Rest[CoefficientList[Series[x(1+10x)(100x^2-10x+1)/((100x-1)(x-1)),{x,0,20}],x]] (* or *) Join[{1,101},Table[FromDigits[Join[{1,0},PadRight[ {},2n+1,1],{0,1}]],{n,0,20}]] (* Harvey P. Dale, Dec 26 2014 *)

Formula

G.f.: x*(1+10*x)*(100*x^2-10*x+1)/((100*x-1)*(x-1)). - R. J. Mathar, Aug 24 2011

A152764 Bisection of A138144.

Original entry on oeis.org

1, 111, 11011, 1100011, 110000011, 11000000011, 1100000000011, 110000000000011, 11000000000000011, 1100000000000000011, 110000000000000000011, 11000000000000000000011
Offset: 1

Views

Author

Omar E. Pol, Dec 14 2008

Keywords

Examples

			n ...... a(n)
1 ....... 1
2 ...... 111
3 ..... 11011
4 .... 1100011
5 ... 110000011

Links

Crossrefs

Cf. A135577, A138120, A138146, A152756, A152758, A058764.

Programs

  • Mathematica
    LinearRecurrence[{101,-100},{1,111,11011,1100011},20] (* Harvey P. Dale, Nov 26 2019 *)
  • PARI
    Vec(-x*(10*x-1)*(10*x+1)^2/((x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Sep 16 2013

Formula

From Colin Barker, Sep 16 2013: (Start)
a(n) = 11+11*10^(2*n-3) for n>2.
a(n) = 101*a(n-1)-100*a(n-2) for n>4.
G.f.: -x*(10*x-1)*(10*x+1)^2 / ((x-1)*(100*x-1)). (End)

A153500 First 3 terms coincide with A152756. For n>3, a(n) is the palindromic number formed from concatenation of 1, 0, A147759(n-3), 0, A147759(n-3), 0 and 1.

Original entry on oeis.org

1, 101, 10001, 1010101, 101101101, 10101010101, 1010010100101, 101010101010101, 10101101010110101, 1010101010101010101, 101010010101010010101, 10101010101010101010101, 1010101101010101011010101, 101010101010101010101010101, 10101010010101010101001010101
Offset: 1

Views

Author

Omar E. Pol, Dec 27 2008, Feb 18 2009

Keywords

Comments

a(n) is also A153499(n) written in base 2.

Examples

			n ............ a(n)
1 ............. 1
2 ............ 101
3 ........... 10001
4 .......... 1010101
5 ......... 101101101
6 ........ 10101010101
7 ....... 1010010100101
8 ...... 101010101010101
9 ..... 10101101010110101
10 ... 1010101010101010101
======================================
Another visualization of the structure
======================================
1 ............. *
2 ............ /.\
3 ........... /...\
4 .......... /.*.*.\
5 ......... /./|.|\.\
6 ........ /./.|.|.\.\
7 ....... /./..|.|..\.\
8 ...... /./.*.|.|.*.\.\
9 ..... /././|.|.|.|\.\.\
10 ... /././.|.|.|.|.\.\.\

Links

Crossrefs

Cf. A135577, A138146, A152576, A152764, A153497, A153498, A153499, A144564.

Formula

a(n) = 101*a(n-1)-1110*a(n-2)+102010*a(n-3)-111000*a(n-4)+1010000*a(n-5)-1000000*a(n-6), n>7. [R. J. Mathar, Feb 20 2009]
G.f.: -x*(1000000*x^6-1010000*x^5+10000*x^4-10100*x^3-910*x^2-1) / ((x-1)*(100*x-1)*(10*x^2+1)*(1000*x^2+1)). [Colin Barker, Sep 17 2013]

Extensions

More terms from R. J. Mathar, Feb 20 2009
Keyword:base added by Charles R Greathouse IV, Apr 26 2010
More terms from Colin Barker, Sep 17 2013
Previous Showing 11-14 of 14 results.

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

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