A003333 - OEIS

%I #24 Oct 21 2023 18:23:31

%S 10,17,24,31,36,38,43,45,50,52,57,59,62,64,66,69,71,73,76,78,80,83,85,

%T 87,88,90,92,94,95,97,99,101,102,104,106,108,109,111,113,114,115,116,

%U 118,120,121,122,123,125,127,128,129,130,132,134,135,136,137,139,140,141,142

%N Numbers that are the sum of 10 positive cubes.

%C 374 is the largest of only 99 positive integers not in this sequence. - _M. F. Hasler_, Aug 13 2020

%H David A. Corneth, <a href="/A003333/b003333.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

%H OEIS Wiki, <a href="/wiki/Index_to_Sums_of_like_powers">Index to sequences related to sums of like powers</a>.

%F a(n) = n + 99 for all n > 275. - _M. F. Hasler_, Aug 13 2020

%e From _David A. Corneth_, Aug 01 2020: (Start)

%e 1646 is in the sequence as 1646 = 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 7^3 + 7^3 +  8^3.

%e 2790 is in the sequence as 2790 = 4^3 + 4^3 + 5^3 + 5^3 + 5^3 + 6^3 + 6^3 + 7^3 + 8^3 + 10^3.

%e 3450 is in the sequence as 3450 = 5^3 + 5^3 + 5^3 + 5^3 + 5^3 + 7^3 + 8^3 + 8^3 + 9^3 +  9^3. (End)

%o (PARI) (A003333_upto(N)=select( {is_A003333(n,k=10,m=3,L=sqrtnint(abs(n-k+1),m))=if( n>k*L^m || n<k, 0, n<k*L^m, forstep(r=min(k-1,n\L^m),0,-1, self()(n-r*L^m,k-r,m,L-1) && return(1)), 1)}, [1..N]))(200) \\ _M. F. Hasler_, Aug 02 2020

%o A3333=A003333_upto(320); A003333(n)=if(n>275, n+99, n>222, n+98, A3333[n]) \\ _M. F. Hasler_, Aug 13 2020

%Y Other sequences of numbers that are the sum of x nonzero y-th powers:

%Y   A000404 (x=2, y=2), A000408 (3, 2), A000414 (4, 2), A047700 (5, 2),

%Y   A003325 (2, 3), A003072 (3, 3), A003327 .. A003335 (4 .. 12, 3),

%Y   A003336 .. A003346 (2 .. 12, 4), A003347 .. A003357 (2 .. 12, 5),

%Y   A003358 .. A003368 (2 .. 12, 6), A003369 .. A003379 (2 .. 12, 7),

%Y   A003380 .. A003390 (2 .. 12, 8), A003391 .. A004801 (2 .. 12, 9),

%Y   A004802 .. A004812 (2 .. 12, 10), A004813 .. A004823 (2 .. 12, 11).

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_