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 1-4 of 4 results.

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

A186676 Total number of n-digit numbers requiring 15 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 6, 60, 624, 6071, 60073, 600069, 6000069, 60000069, 600000061, 6000000071
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) + a(n) + A186678(n) + A186681(n) + A186683(n) + A186685(n) = A052268(n), for n>1.

Links

Crossrefs

Cf. A046046, A186675.

Formula

a(n) = A186675(n) - A186675(n-1).

Extensions

a(5)-a(11) from Giovanni Resta, Apr 29 2016

A046047 Sum of 16 but no fewer nonzero fourth powers.

Original entry on oeis.org

31, 46, 61, 76, 111, 126, 141, 156, 191, 206, 221, 236, 271, 286, 301, 316, 351, 366, 381, 396, 431, 446, 461, 476, 496, 511, 526, 541, 556, 591, 606, 621, 671, 686, 701, 736, 751, 766, 781, 831, 846, 861, 911, 926, 941, 976, 991, 1006, 1021, 1071, 1086
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

What is the least k such that the sequence "Sum of k but no fewer nonzero fourth powers." is finite? - David A. Corneth, Jun 24 2018
13792 is the last number requiring 17 nonzero fourth powers. This sequence is infinite since numbers of the form 31*16^e always require 16 but no fewer. - Jianing Song, Jul 08 2018

Links

Crossrefs

Cf. A000583, A002377, A046046, A046048, A099591.

Programs

  • Mathematica
    Select[Range[  1100], (pr = PowersRepresentations[#, 16, 4]; test = pr != {} && Count[pr, r_ /; (Times @@ r) == 0] == 0; If[test, Print[#]]; test) &] (* Jean-François Alcover, Oct 30 2012 *)

Extensions

More terms from Arlin Anderson (starship1(AT)gmail.com)

A085304 Least number of 4th powers required to represent n!.

Original entry on oeis.org

1, 1, 2, 6, 9, 10, 15, 15, 9, 10, 15, 6, 12, 12
Offset: 0

Views

Author

Labos Elemer, Jun 30 2003

Keywords

Examples

			n=6: 6!=720=625+81+14,length-of-solution=16>=a(6)
but 6!=720=2.256+13.16 seems shortest solution a(6)=15
after, see also A046046
n=7: 7!=5040=3.1296+4.256+8.16 so a(7)<=15 (uncertain);
n=8: a(8)<=9 because 8!=4.10000+1.256+4.16.

Links

Crossrefs

Cf. A000142, A084355, A060387, A003336-A003346, A046046, A046044-A046050.

Formula

"Shortest" solutions to n!=Sum[x(j)^4], j=1, .., m[n] with minimal value of m[n]: a(n)=Min{m[n]}. Per analogiam A084355.

Extensions

a(7)-a(11) from John W. Layman, Aug 13 2004
a(12) from Sean A. Irvine, Feb 11 2010
a(13) from Sean A. Irvine, Feb 15 2010
Showing 1-4 of 4 results.

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