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.

A186663 Total number of positive integers below 10^n requiring 9 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

1, 6, 78, 920, 8675, 77225, 691255, 6705498, 66719462, 666733325, 6666747237
Offset: 1

Views

Author

Martin Renner, Feb 25 2011

Keywords

Comments

A114322(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + a(n) + A186665(n) + A186667(n) + A186669(n) + A186671(n) + A186673(n) + A186675(n) + A186677(n) + A186680(n) + A186682(n) + A186684(n) = A002283(n)

Links

Crossrefs

Cf. A003343, A186664.

Extensions

a(5)-a(8) from Lars Blomberg, May 08 2011
a(9) from Hiroaki Yamanouchi, Oct 13 2014
a(10)-a(11) from Giovanni Resta, Apr 26 2016

A186665 Total number of positive integers below 10^n requiring 10 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 6, 72, 812, 7876, 70630, 673358, 6676098, 66678723, 666681488, 6666684311
Offset: 1

Views

Author

Martin Renner, Feb 25 2011

Keywords

Comments

A114322(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + a(n) + A186667(n) + A186669(n) + A186671(n) + A186673(n) + A186675(n) + A186677(n) + A186680(n) + A186682(n) + A186684(n) = A002283(n).

Links

Crossrefs

Cf. A003344, A186666.

Extensions

a(5)-a(7) from Lars Blomberg, May 08 2011
a(8)-a(9) from Hiroaki Yamanouchi, Oct 13 2014
a(10)-a(11) from Giovanni Resta, Apr 26 2016

A186667 Total number of positive integers below 10^n requiring 11 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 6, 70, 760, 7434, 68348, 669289, 6670284, 66671226, 666672168, 6666673077
Offset: 1

Views

Author

Martin Renner, Feb 25 2011

Keywords

Comments

A114322(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + A186665(n) + a(n) + A186669(n) + A186671(n) + A186673(n) + A186675(n) + A186677(n) + A186680(n) + A186682(n) + A186684(n) = A002283(n).

Links

Crossrefs

Cf. A003345, A186668.

Extensions

a(5)-a(7) from Lars Blomberg, May 08 2011
a(8)-a(9) from Hiroaki Yamanouchi, Oct 13 2014
a(10)-a(11) from Giovanni Resta, Apr 29 2016

A186671 Total number of positive integers below 10^n requiring 13 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 6, 66, 706, 6945, 67173, 667369, 6667582, 66667813, 666668052, 6666668292
Offset: 1

Views

Author

Martin Renner, Feb 25 2011

Keywords

Comments

A114322(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + A186665(n) + A186667(n) + A186669(n) + a(n) + A186673(n) + A186675(n) + A186677(n) + A186680(n) + A186682(n) + A186684(n) = A002283(n).

Links

Crossrefs

Cf. A046044, A186672.

Extensions

a(5)-a(6) from Lars Blomberg, May 08 2011
a(7) from Charles R Greathouse IV, May 08 2011
a(8)-a(9) from Hiroaki Yamanouchi, Oct 13 2014
a(10)-a(11) from Giovanni Resta, Apr 29 2016

A186673 Total number of positive integers below 10^n requiring 14 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 6, 66, 698, 6833, 66965, 667080, 6667198, 66667327, 666667454, 6666667590
Offset: 1

Views

Author

Martin Renner, Feb 25 2011

Keywords

Comments

A114322(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + A186665(n) + A186667(n) + A186669(n) + A186671(n) + a(n) + A186675(n) + A186677(n) + A186680(n) + A186682(n) + A186684(n) = A002283(n)

Links

Crossrefs

Cf. A046045, A186674.

Extensions

a(5)-a(6) from Lars Blomberg, May 08 2011
a(7) from Charles R Greathouse IV, May 08 2011
a(8)-a(9) from Hiroaki Yamanouchi, Oct 13 2014
a(10)-a(11) from Giovanni Resta, Apr 29 2016

A186675 Total number of positive integers below 10^n requiring 15 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 6, 66, 690, 6761, 66834, 666903, 6666972, 66667041, 666667102, 6666667173
Offset: 1

Views

Author

Martin Renner, Feb 25 2011

Keywords

Comments

A114322(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + A186665(n) + A186667(n) + A186669(n) + A186671(n) + A186673(n) + a(n) + A186677(n) + A186680(n) + A186682(n) + A186684(n) = A002283(n)

Links

Crossrefs

Cf. A046046, A186676.

Extensions

a(5)-a(6) from Lars Blomberg, May 08 2011
a(7) from Charles R Greathouse IV, May 08 2011
a(8)-a(9) from Hiroaki Yamanouchi, Oct 13 2014
a(10)-a(11) from Giovanni Resta, Apr 29 2016

A186680 Total number of positive integers below 10^n requiring 17 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 3, 33, 63, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65
Offset: 1

Views

Author

Martin Renner, Feb 25 2011

Keywords

Comments

A114322(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + A186665(n) + A186667(n) + A186669(n) + A186671(n) + A186673(n) + A186675(n) + A186677(n) + a(n) + A186682(n) + A186684(n) = A002283(n)
a(n) = 65 for n >= 5. - Nathaniel Johnston, May 09 2011
Continued fraction expansion of (826055+sqrt(4229))/2503382. - Bruno Berselli, May 10 2011

Links

Crossrefs

Cf. A046048, A099591.

Programs

  • Mathematica
    PadRight[{0, 3, 33, 63}, 100, 65] (* Paolo Xausa, Jul 31 2024 *)

Formula

G.f.: x^2*(3+30*x+30*x^2+2*x^3)/(1-x). - Bruno Berselli, May 10 2011

Extensions

a(5)-a(6) from Lars Blomberg, May 08 2011
a(7) from Charles R Greathouse IV, May 08 2011
Terms after a(7) from Nathaniel Johnston, May 09 2011

A186682 Total number of positive integers below 10^n requiring 18 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 2, 19, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24
Offset: 1

Views

Author

Martin Renner, Feb 25 2011

Keywords

Comments

A114322(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + A186665(n) + A186667(n) + A186669(n) + A186671(n) + A186673(n) + A186675(n) + A186677(n) + A186680(n) + a(n) + A186684(n) = A002283(n)
a(n) = 24 for n >= 4. - Nathaniel Johnston, May 09 2011
Continued fraction expansion of (185-sqrt(145))/355. - Bruno Berselli, May 10 2011

Links

Crossrefs

Cf. A046049.

Programs

  • Mathematica
    PadRight[{0, 2, 19}, 100, 24] (* Paolo Xausa, Jul 30 2024 *)

Formula

G.f.: x^2*(2+17*x+5*x^2)/(1-x). - Bruno Berselli, May 10 2011

Extensions

a(5)-a(6) from Lars Blomberg, May 08 2011
a(7) from Charles R Greathouse IV, May 08 2011
Terms after a(7) from Nathaniel Johnston, May 09 2011

A186678 Total number of n-digit numbers requiring 16 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 4, 43, 241, 299, 287, 304, 309, 316, 286, 299
Offset: 1

Views

Author

Martin Renner, Feb 25 2011

Keywords

Comments

A102831(n) + A186650(n) + A186652(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + A186674(n) + A186676(n) + a(n) + A186681(n) + A186683(n) + A186685(n) = A052268(n), for n>1.

Links

Crossrefs

Cf. A046047, A186677.

Formula

a(n) = A186677(n) - A186677(n-1).

Extensions

a(5)-a(11) from Giovanni Resta, Apr 29 2016
Previous Showing 11-19 of 19 results.

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