A155015
Integer part of square root of n^11 = A008455(n).
Original entry on oeis.org
0, 1, 45, 420, 2048, 6987, 19047, 44467, 92681, 177147, 316227, 534145, 861979, 1338715, 2012353, 2941046, 4194304, 5854220, 8016758, 10793065, 14310835, 18715701, 24172676, 30867616, 39008731, 48828125, 60583368, 74559107
Offset: 0
-
[Floor(Sqrt(n^11)): n in [1..30]]; // G. C. Greubel, Dec 30 2017
-
a={};Do[AppendTo[a,IntegerPart[(n^11)^(1/2)]],{n,0,5!}];a
Table[Floor[Sqrt[n^11]], {n,1,30}] (* G. C. Greubel, Dec 30 2017 *)
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for(n=1,30, print1(floor(sqrt(n^11)), ", ")) \\ G. C. Greubel, Dec 30 2017
A253711
Second partial sums of 11th powers (A008455).
Original entry on oeis.org
1, 2050, 181246, 4554746, 57756371, 473755052, 2867080476, 13850340492, 56214660117, 198578979742, 626254969978, 1796939330902, 4759784085863, 11772194010488, 27434359794488, 60688711622904, 128214959758953, 260009617974234, 508294535087734, 961379452201234, 1764741869856955, 3152422588924004, 5492913065904980
Offset: 1
- Luciano Ancora, Recurrence relation for the second partial sums of m-th powers
- Luciano Ancora, Second partial sums of the m-th powers
- Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
-
Table[n (n + 1) (n + 2) (70 n^10 + 700 n^9 + 2310 n^8 + 1680 n^7 - 4655 n^6 - 4410 n^5 + 8240 n^4 + 4120 n^3 - 7819 n^2 + 202 n + 1382)/10920, {n, 1, 20}] (* Vincenzo Librandi, Jan 15 2015 *)
RecurrenceTable[{a[n] == 2 a[n - 1] - a[n - 2] + n^11, a[1] == 1, a[2] == 2050}, a, {n, 1, 20}] (* Bruno Berselli, Jan 15 2015 *)
A004823
Numbers that are the sum of 12 positive 11th powers.
Original entry on oeis.org
12, 2059, 4106, 6153, 8200, 10247, 12294, 14341, 16388, 18435, 20482, 22529, 24576, 177158, 179205, 181252, 183299, 185346, 187393, 189440, 191487, 193534, 195581, 197628, 199675, 354304, 356351, 358398, 360445, 362492, 364539, 366586, 368633, 370680, 372727, 374774
Offset: 1
From _David A. Corneth_, Aug 04 2020: (Start)
208428902 is in the sequence as 208428902 = 1^11 + 2^11 + 3^11 + 3^11 + 3^11 + 4^11 + 4^11 + 4^11 + 5^11 + 5^11 + 5^11 + 5^11.
562491247 is in the sequence as 562491247 = 2^11 + 2^11 + 2^11 + 2^11 + 2^11 + 3^11 + 4^11 + 5^11 + 5^11 + 5^11 + 5^11 + 6^11.
620052034 is in the sequence as 620052034 = 3^11 + 3^11 + 3^11 + 4^11 + 4^11 + 4^11 + 5^11 + 5^11 + 5^11 + 5^11 + 5^11 + 6^11. (End)
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Select[Union[Total[#^11]&/@Tuples[Range[3],{12}]],#<+400000&] (* Harvey P. Dale, Apr 29 2011 *)
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A004823_upto(N, n=12, p=11)=my(P=[x^p|x<-[1..sqrtnint(N-n+1, p)]], S=P); while(n--, S=Set(concat([[x+y|y<-S,x+y<=N]|x<-P])));S \\ M. F. Hasler, Jul 03 2025
A004816
Numbers that are the sum of 5 positive 11th powers.
Original entry on oeis.org
5, 2052, 4099, 6146, 8193, 10240, 177151, 179198, 181245, 183292, 185339, 354297, 356344, 358391, 360438, 531443, 533490, 535537, 708589, 710636, 885735, 4194308, 4196355, 4198402, 4200449, 4202496, 4371454, 4373501, 4375548, 4377595, 4548600, 4550647, 4552694, 4725746
Offset: 1
From _David A. Corneth_, Aug 04 2020: (Start)
100004375547 is in the sequence as 100004375547 = 2^11 + 2^11 + 3^11 + 4^11 + 10^11.
385311851854 is in the sequence as 385311851854 = 2^11 + 2^11 + 3^11 + 10^11 + 11^11.
743742353408 is in the sequence as 743742353408 = 4^11 + 4^11 + 6^11 + 6^11 + 12^11. (End)
A004817
Numbers that are the sum of 6 positive 11th powers.
Original entry on oeis.org
6, 2053, 4100, 6147, 8194, 10241, 12288, 177152, 179199, 181246, 183293, 185340, 187387, 354298, 356345, 358392, 360439, 362486, 531444, 533491, 535538, 537585, 708590, 710637, 712684, 885736, 887783, 1062882, 4194309, 4196356, 4198403, 4200450, 4202497, 4204544, 4371455
Offset: 1
4817
From _David A. Corneth_, Aug 04 2020: (Start)
8953440236 is in the sequence as 8953440236 = 3^11 + 3^11 + 3^11 + 3^11 + 6^11 + 8^11.
64837279358 is in the sequence as 64837279358 = 3^11 + 5^11 + 5^11 + 7^11 + 9^11 + 9^11.
131385255963 is in the sequence as 131385255963 = 1^11 + 1^11 + 2^11 + 4^11 + 9^11 + 10^11. (End)
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With[{nn=5},Select[Union[Total/@Tuples[Range[nn]^11,{6}]],#<=nn^11+5&]] (* Harvey P. Dale, Jun 30 2020 *)
A004818
Numbers that are the sum of 7 positive 11th powers.
Original entry on oeis.org
7, 2054, 4101, 6148, 8195, 10242, 12289, 14336, 177153, 179200, 181247, 183294, 185341, 187388, 189435, 354299, 356346, 358393, 360440, 362487, 364534, 531445, 533492, 535539, 537586, 539633, 708591, 710638, 712685, 714732, 885737, 887784, 889831, 1062883, 1064930, 1240029
Offset: 1
From _David A. Corneth_, Aug 04 2020: (Start)
8638762722 is in the sequence as 8638762722 = 1^11 + 1^11 + 1^11 + 1^11 + 1^11 + 5^11 + 8^11.
10930416781 is in the sequence as 10930416781 = 2^11 + 2^11 + 3^11 + 3^11 + 6^11 + 7^11 + 8^11.
29728651567 is in the sequence as 29728651567 = 1^11 + 4^11 + 7^11 + 7^11 + 8^11 + 8^11 + 8^11. (End)
A004819
Numbers that are the sum of 8 positive 11th powers.
Original entry on oeis.org
8, 2055, 4102, 6149, 8196, 10243, 12290, 14337, 16384, 177154, 179201, 181248, 183295, 185342, 187389, 189436, 191483, 354300, 356347, 358394, 360441, 362488, 364535, 366582, 531446, 533493, 535540, 537587, 539634, 541681, 708592, 710639, 712686, 714733, 716780, 885738
Offset: 1
From _David A. Corneth_, Aug 04 2020: (Start)
2353238152 is in the sequence as 2353238152 = 3^11 + 3^11 + 3^11 + 4^11 + 4^11 + 4^11 + 6^11 + 7^11.
8594130949 is in the sequence as 8594130949 = 1^11 + 1^11 + 1^11 + 1^11 + 1^11 + 2^11 + 4^11 + 8^11.
9050746288 is in the sequence as 9050746288 = 2^11 + 2^11 + 3^11 + 3^11 + 5^11 + 5^11 + 6^11 + 8^11. (End)
A004820
Numbers that are the sum of 9 positive 11th powers.
Original entry on oeis.org
9, 2056, 4103, 6150, 8197, 10244, 12291, 14338, 16385, 18432, 177155, 179202, 181249, 183296, 185343, 187390, 189437, 191484, 193531, 354301, 356348, 358395, 360442, 362489, 364536, 366583, 368630, 531447, 533494, 535541, 537588, 539635, 541682, 543729, 708593, 710640
Offset: 1
From _David A. Corneth_, Aug 04 2020: (Start)
1088578555 is in the sequence as 1088578555 = 2^11 + 2^11 + 2^11 + 2^11 + 2^11 + 3^11 + 6^11 + 6^11 + 6^11.
2345030787 is in the sequence as 2345030787 = 2^11 + 2^11 + 3^11 + 3^11 + 3^11 + 3^11 + 4^11 + 6^11 + 7^11.
4326193446 is in the sequence as 4326193446 = 1^11 + 1^11 + 3^11 + 3^11 + 4^11 + 4^11 + 6^11 + 7^11 + 7^11. (End)
A004821
Numbers that are the sum of 10 positive 11th powers.
Original entry on oeis.org
10, 2057, 4104, 6151, 8198, 10245, 12292, 14339, 16386, 18433, 20480, 177156, 179203, 181250, 183297, 185344, 187391, 189438, 191485, 193532, 195579, 354302, 356349, 358396, 360443, 362490, 364537, 366584, 368631, 370678, 531448, 533495, 535542, 537589, 539636, 541683
Offset: 1
From _David A. Corneth_, Aug 04 2020: (Start)
432600798 is in the sequence as 432600798 = 1^11 + 2^11 + 2^11 + 4^11 + 4^11 + 4^11 + 4^11 + 4^11 + 5^11 + 6^11.
1695330897 is in the sequence as 1695330897 = 2^11 + 5^11 + 5^11 + 5^11 + 5^11 + 5^11 + 6^11 + 6^11 + 6^11 + 6^11.
2075516485 is in the sequence as 2075516485 = 1^11 + 1^11 + 1^11 + 2^11 + 3^11 + 3^11 + 3^11 + 5^11 + 5^11 + 7^11. (End)
A004822
Numbers that are the sum of 11 positive 11th powers.
Original entry on oeis.org
11, 2058, 4105, 6152, 8199, 10246, 12293, 14340, 16387, 18434, 20481, 22528, 177157, 179204, 181251, 183298, 185345, 187392, 189439, 191486, 193533, 195580, 197627, 354303, 356350, 358397, 360444, 362491, 364538, 366585, 368632, 370679, 372726, 531449, 533496, 535543
Offset: 1
From _David A. Corneth_, Aug 01 2020: (Start)
460807606 is in the sequence as 460807606 = 1^11 + 1^11 + 1^11 + 1^11 + 1^11 + 1^11 + 3^11 + 3^11 + 5^11 + 5^11 + 6^11.
795925198 is in the sequence as 795925198 = 3^11 + 3^11 + 3^11 + 4^11 + 4^11 + 4^11 + 4^11 + 4^11 + 5^11 + 6^11 + 6^11.
1504395992 is in the sequence as 1504395992 = 2^11 + 2^11 + 2^11 + 2^11 + 3^11 + 4^11 + 5^11 + 6^11 + 6^11 + 6^11 + 6^11. (End)
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).
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M = 6347807907; m = M^(1/11) // 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++, For[i = h, i <= m, i++,
For[j = i, j <= m, j++, For[k = j, k <= m, k++,
s = a^11+b^11+c^11+d^11+e^11+f^11+g^11+h^11+i^11+j^11+k^11;
If[s <= M, Sow[s]]]]]]]]]]]]]][[2, 1]] // Union (* Jean-François Alcover, Dec 01 2020 *)
Showing 1-10 of 43 results.
Comments