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 1-3 of 3 results.

A153497 a(n) is the number whose binary expansion is A153498(n).

Original entry on oeis.org

1, 7, 21, 73, 341, 1453, 5461, 21157, 87381, 354997, 1398101, 5548693, 22369621, 89828053, 357913941, 1428859477, 5726623061, 22928862037, 91625968981, 366324918613, 1466015503701, 5865493671253, 23456248059221, 93813538989397
Offset: 1

Views

Author

Omar E. Pol, Dec 27 2008

Keywords

Links

Crossrefs

Cf. A135576, A153498, A153499, A153500.

Programs

  • Mathematica
    LinearRecurrence[{5,-14,50,-56,80,-64},{1,7,21,73,341,1453},30] (* Harvey P. Dale, Nov 21 2012 *)

Formula

From R. J. Mathar, Feb 20 2009: (Start)
a(n) = 5*a(n-1) - 14*a(n-2) + 50*a(n-3) - 56*a(n-4) + 80*a(n-5) - 64*a(n-6).
G.f.: x*(1 +2x +16x^3 -24x^4 +32x^5)/((1-x)*(1-4x)*(1+2x^2)*(1+8x^2)). (End)

Extensions

More terms from R. J. Mathar, Feb 20 2009

A153499 a(n) is the number whose binary expansion is A153500(n).

Original entry on oeis.org

1, 5, 17, 85, 365, 1365, 5285, 21845, 88757, 349525, 1387157, 5592405, 22457045, 89478485, 357214805, 1431655765, 5732215637, 22906492245, 91581229397, 366503875925, 1466373418325, 5864062014805, 23453384746325, 93824992236885
Offset: 1

Views

Author

Omar E. Pol, Dec 27 2008

Keywords

Comments

Empirical g.f. confirmed similar to A153497 and A153498. - Ray Chandler, Oct 15 2024

Links

Crossrefs

Cf. A135576, A153497, A153498, A153500.

Formula

Empirical g.f.: -x*(64*x^6-80*x^5+16*x^4-20*x^3-6*x^2-1) / ((x-1)*(4*x-1)*(2*x^2+1)*(8*x^2+1)). - Colin Barker, Sep 17 2013

Extensions

More terms from R. J. Mathar, Feb 20 2009

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
Showing 1-3 of 3 results.

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

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