A181376 - OEIS

%I #25 Apr 18 2019 22:05:05

%S 2,7,32,161,736,3416,15976,74295,345334,1605089,7455698,34623338,

%T 160759047,746318897,3464508951,16081935250,74648713406

%N Total number of n-digit numbers requiring 2 positive cubes in their representation as a sum of cubes.

%C A181354(n) + a(n) + A181378(n) + A181380(n) + A181384(n) + A181401(n) + A181403(n) + A181405(n) + A171386(n) = A052268(n).

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/WaringsProblem.html">MathWorld -- Waring's Problem.</a>

%F a(n) = A181375(n)-A181375(n-1).

%e a(1) = 2 from 1+1=2, 1+8=9.

%e a(2) = 7 from 8+8=16, 1+27=28, 35, 54, 65, 72, 91.

%t Table[Length[c = Table[j^3, {j, (10^n - 1)^(1/3)}];

%t   Select[Union[Flatten[Outer[Plus, c, c]]],

%t IntervalMemberQ[Interval[{10^(n - 1), 10^n - 1}], #] &]], {n, 10}] (* _Robert Price_, Apr 18 2019 *)

%o (PARI) a(n)=my(N=10^n, Nn=N/10, v=List(), x3, t); sum(x=sqrtnint(Nn\2,3), sqrtnint(N-1, 3), x3=x^3; sum(y=1, min(sqrtnint(N-x3, 3), x), t=x3+y^3; t>=Nn && !ispower(t, 3) && listput(v, t))); #vecsort(v, , 8) \\ _Charles R Greathouse IV_, Oct 16 2013

%Y Cf. A003325.

%K nonn,more,base

%O 1,1

%A _Martin Renner_, Jan 28 2011

%E a(6)-a(11) from _Charles R Greathouse IV_, Oct 16 2013

%E a(12) from _Lars Blomberg_, Jan 15 2014

%E a(13)-a(17) from _Hiroaki Yamanouchi_, Jul 13 2014