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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A003386 Numbers that are the sum of 8 nonzero 8th powers.

Original entry on oeis.org

8, 263, 518, 773, 1028, 1283, 1538, 1793, 2048, 6568, 6823, 7078, 7333, 7588, 7843, 8098, 8353, 13128, 13383, 13638, 13893, 14148, 14403, 14658, 19688, 19943, 20198, 20453, 20708, 20963, 26248, 26503, 26758, 27013, 27268, 32808, 33063, 33318, 33573
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

As the order of addition doesn't matter we can assume terms are in nondecreasing order. - David A. Corneth, Aug 01 2020

Examples

			From _David A. Corneth_, Aug 01 2020: (Start)
9534597 is in the sequence as 9534597 = 2^8 + 3^8 + 3^8 + 3^8 + 5^8 + 6^8 + 6^8 + 7^8.
13209988 is in the sequence as 13209988 = 1^8 + 1^8 + 2^8 + 2^8 + 2^8 + 6^8 + 7^8 + 7^8.
19046628 is in the sequence as 19046628 = 2^8 + 2^8 + 3^8 + 4^8 + 6^8 + 7^8 + 7^8 + 7^8. (End)

Links

Crossrefs

A###### (x, y): Numbers that are the form of x nonzero y-th powers.
Cf. A000404 (2, 2), A000408 (3, 2), A000414 (4, 2), A003072 (3, 3), A003325 (3, 2), A003327 (4, 3), A003328 (5, 3), A003329 (6, 3), A003330 (7, 3), A003331 (8, 3), A003332 (9, 3), A003333 (10, 3), A003334 (11, 3), A003335 (12, 3), A003336 (2, 4), A003337 (3, 4), A003338 (4, 4), A003339 (5, 4), A003340 (6, 4), A003341 (7, 4), A003342 (8, 4), A003343 (9, 4), A003344 (10, 4), A003345 (11, 4), A003346 (12, 4), A003347 (2, 5), A003348 (3, 5), A003349 (4, 5), A003350 (5, 5), A003351 (6, 5), A003352 (7, 5), A003353 (8, 5), A003354 (9, 5), A003355 (10, 5), A003356 (11, 5), A003357 (12, 5), A003358 (2, 6), A003359 (3, 6), A003360 (4, 6), A003361 (5, 6), A003362 (6, 6), A003363 (7, 6), A003364 (8, 6), A003365 (9, 6), A003366 (10, 6), A003367 (11, 6), A003368 (12, 6), A003369 (2, 7), A003370 (3, 7), A003371 (4, 7), A003372 (5, 7), A003373 (6, 7), A003374 (7, 7), A003375 (8, 7), A003376 (9, 7), A003377 (10, 7), A003378 (11, 7), A003379 (12, 7), A003380 (2, 8), A003381 (3, 8), A003382 (4, 8), A003383 (5, 8), A003384 (6, 8), A003385 (7, 8), A003387 (9, 8), A003388 (10, 8), A003389 (11, 8), A003390 (12, 8), A003391 (2, 9), A003392 (3, 9), A003393 (4, 9), A003394 (5, 9), A003395 (6, 9), A003396 (7, 9), A003397 (8, 9), A003398 (9, 9), A003399 (10, 9), A004800 (11, 9), A004801 (12, 9), A004802 (2, 10), A004803 (3, 10), A004804 (4, 10), A004805 (5, 10), A004806 (6, 10), A004807 (7, 10), A004808 (8, 10), A004809 (9, 10), A004810 (10, 10), A004811 (11, 10), A004812 (12, 10), A004813 (2, 11), A004814 (3, 11), A004815 (4, 11), A004816 (5, 11), A004817 (6, 11), A004818 (7, 11), A004819 (8, 11), A004820 (9, 11), A004821 (10, 11), A004822 (11, 11), A004823 (12, 11), A047700 (5, 2).

Programs

  • Mathematica
    M = 92646056; m = M^(1/8) // Ceiling; Reap[
For[a = 1, a <= m, a++, For[b = a, b <= m, b++, For[c = b, c <= m, c++,
For[d = c, d <= m, d++, For[e = d, e <= m, e++, For[f = e, f <= m, f++,
For[g = f, g <= m, g++, For[h = g, h <= m, h++,
s = a^8 + b^8 + c^8 + d^8 + e^8 + f^8 + g^8 + h^8;
If[s <= M, Sow[s]]]]]]]]]]][[2, 1]] // Union (* Jean-François Alcover, Dec 01 2020 *)

Extensions

b-file checked by R. J. Mathar, Aug 01 2020
Incorrect program removed by David A. Corneth, Aug 01 2020

A047723 Sum of 12 but no fewer nonzero fourth powers.

Original entry on oeis.org

12, 27, 42, 57, 72, 92, 107, 122, 137, 152, 172, 187, 192, 202, 217, 232, 252, 267, 282, 297, 312, 332, 347, 362, 377, 392, 412, 427, 432, 442, 457, 472, 492, 497, 507, 522, 537, 552, 572, 587, 602, 617, 636, 652, 667, 672, 682, 697, 716, 732, 747, 762
Offset: 1

Views

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

Links

Crossrefs

Cf. A000583, A002377, A003346, A046044.

Programs

  • Python
    from itertools import count, takewhile, combinations_with_replacement as mc
def aupto(limit):
    qd = list(takewhile(lambda x: x <= limit, (k**4 for k in count(1))))
    ss = [set(sum(c) for c in mc(qd, i)) for i in range(13)]
    for i in range(11, 0, -1): ss[12] -= ss[i]
    return sorted(s for s in ss[12] if s <= limit)
print(aupto(762)) # Michael S. Branicky, Dec 27 2021

Extensions

Typo in data corrected by D. S. McNeil, Aug 17 2010

A047724 Sum of 13 nonzero fourth powers.

Original entry on oeis.org

13, 28, 43, 58, 73, 88, 93, 103, 108, 118, 123, 133, 138, 148, 153, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 228, 233, 243, 248, 253, 258, 263, 268, 273, 278, 283, 293, 298, 308, 313, 323, 328, 333, 338, 343, 348, 358, 363, 373, 378, 388
Offset: 1

Views

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

Crossrefs

Cf. A000583, A003346, A046044.

Programs

  • Mathematica
    Union[Total/@Tuples[Range[3]^4,13]] (* Harvey P. Dale, Nov 04 2015 *)

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
Previous Showing 41-44 of 44 results.

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

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