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 41-44 of 44 results.

A155468 Numbers that are sums of 8th powers of 2 distinct positive integers.

Original entry on oeis.org

257, 6562, 6817, 65537, 65792, 72097, 390626, 390881, 397186, 456161, 1679617, 1679872, 1686177, 1745152, 2070241, 5764802, 5765057, 5771362, 5830337, 6155426, 7444417, 16777217, 16777472, 16783777, 16842752, 17167841, 18456832, 22542017, 43046722, 43046977, 43053282
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 23 2009

Keywords

Examples

			1^8 + 2^8 = 257, 1^8 + 3^8 = 6562, 2^8 + 3^8 = 6817, ...

Links

Crossrefs

Cf. A003380, A088719 (distinct 7th), A088677 (distinct 6th), A088703, A088687, A024670 (distinct 3rd), A004431 (distinct 2nd).

Programs

  • Mathematica
    lst={};e=8;Do[Do[x=a^e;Do[y=b^e;If[x+y==n,Print[n,",",Date[]];AppendTo[lst,n]],{b,Floor[(n-x)^(1/e)],a+1,-1}],{a,Floor[n^(1/e)],1,-1}],{n,4*8!}];lst
  • PARI
    list(lim)=my(v=List(),t); lim\=1; for(m=2,sqrtnint(lim-1,8), t=m^8; for(n=1,min(sqrtnint(lim-t,8),m-1), listput(v,t+n^8))); Set(v) \\ Charles R Greathouse IV, Nov 05 2017

Extensions

8 more terms. - R. J. Mathar, Sep 07 2017
More terms from Chai Wah Wu, Nov 05 2017

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

A132215 Numbers that are sums of eighth powers of two distinct primes.

Original entry on oeis.org

6817, 390881, 397186, 5765057, 5771362, 6155426, 214359137, 214365442, 214749506, 220123682, 815730977, 815737282, 816121346, 821495522, 1030089602, 6975757697, 6975764002, 6976148066, 6981522242, 7190116322, 7791488162
Offset: 1

Views

Author

Jonathan Vos Post, Aug 13 2007

Keywords

Comments

This is to 8th powers as A132214 is to 7th powers, A130555 is to 6th powers, A130292 is to fifth powers, A130873 is to 4th powers and A120398 is to cubes. These CAN be prime, as the polynomial x^8 + y^8 is irreducible over Z, as seen in A132216. The first such example is a(11) = A132216(1) = 2^8 + 13^8 = 256 + 815730721 = 815730977, which is prime.
A subset of A003380. - R. J. Mathar, May 11 2008

Examples

			a(1) = 2^8 + 3^8 = 256 + 6561 = 6817 = 17 * 401.

Crossrefs

Cf. A000040, A001016, A050997, A120398, A122616, A130873, A130555, A132214, A132216.

Programs

  • Mathematica
    Select[Sort[ Flatten[Table[Prime[n]^8 + Prime[k]^8, {n, 15}, {k, n - 1}]]], # <= Prime[15^8] &]
Total/@Subsets[Prime[Range[10]]^8,{2}]//Sort (* Harvey P. Dale, Jun 27 2017 *)

Formula

{A001016(A000040(i)) + A001016(A000040(j)) for i > j}.

A068537 Numbers which can be written as the sum of 2 like powers (x^n + y^n; n>1 & x,y>0).

Original entry on oeis.org

2, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 28, 29, 32, 33, 34, 35, 37, 40, 41, 45, 50, 52, 53, 54, 58, 61, 64, 65, 68, 72, 73, 74, 80, 82, 85, 89, 90, 91, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 122, 125, 126, 128, 129, 130, 133, 136, 137, 145, 146
Offset: 1

Views

Author

Shawn Schafer (coolrelish(AT)hotmail.com), Mar 22 2002

Keywords

Examples

			2 = 1^2 + 1^2; 5 = 1^2 + 2^2; 8 = 2^2 + 2^2; 9 = 1^3 + 2^3; 10 = 1^2 + 3^2; 13 = 2^2 + 3^2; 16 = 2^3 + 2^3; 17 = 1^2 + 4^2; ..... 33 = 1^5 + 2^5; etc...

Crossrefs

Superset of A000404, A003325, A003336, A003347, A003358, A003369, A003380, A003391.

Extensions

More terms from Michel Marcus, Aug 07 2013
More terms from Sean A. Irvine, Feb 21 2024
Previous Showing 41-44 of 44 results.

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