A181401 -id:A181401 - cp's OEIS frontend

A181354 Number of n-digit perfect cubes.

2, 2, 5, 12, 25, 53, 116, 249, 535, 1155, 2487, 5358, 11545, 24871, 53584, 115444, 248715, 535841, 1154435, 2487154, 5358411, 11544347, 24871542, 53584111, 115443470, 248715414, 535841116, 1154434691, 2487154143, 5358411166

Offset: 1

Martin Renner, Jan 28 2011

a(n) is also the total number of n-digit numbers requiring 1 positive cube in their representation as sum of cubes.
a(n) + A181376(n) + A181378(n) + A181380(n) + A181384(n) + A181401(n) + A181403(n) + A181405(n) + A171386(n) = A052268(n).
Differs from A062941 only at n=1, because 0 is considered a 0-digit, not a 1-digit number here. - R. J. Mathar, Jul 09 2011

Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A000578

a:=n->ceil(10^(n/3))-ceil(10^((n-1)/3));

With[{c = Range[4650000]^3}, Length[#]&/@Table[Select[c, IntegerLength[#] == n &], {n, 20}]] (* Harvey P. Dale, Feb 01 2011 *)
Differences[Ceiling[10^(Range[0, 30]/3)]]

a(n) = A061439(n) - A061439(n-1).

More terms from T. D. Noe, Feb 01 2011

A171386 The characteristic function of 2 and 3: 1 if n is prime such that either n-1 or n+1 is prime, else 0.

Original entry on oeis.org

0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Juri-Stepan Gerasimov, Dec 07 2009

A181354(n) + A181376(n) + A181378(n) + A181380(n) + A181384(n) + A181401(n) + A181403(n) + A181405(n) + a(n) = A052268(n).

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A000007, A010051, A063524.

Join[{0, 1, 1},LinearRecurrence[{1},{0},102]] (* Ray Chandler, Sep 23 2015 *)

a(n)=n==2||n==3 \\ Charles R Greathouse IV, Sep 24 2015

a(n) = A130130(n) - A130130(n-1), for n>0.

Edited by Charles R Greathouse IV, Mar 23 2010

A181376 Total number of n-digit numbers requiring 2 positive cubes in their representation as a sum of cubes.

Original entry on oeis.org

2, 7, 32, 161, 736, 3416, 15976, 74295, 345334, 1605089, 7455698, 34623338, 160759047, 746318897, 3464508951, 16081935250, 74648713406

Offset: 1

Martin Renner, Jan 28 2011

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

			a(1) = 2 from 1+1=2, 1+8=9.
a(2) = 7 from 8+8=16, 1+27=28, 35, 54, 65, 72, 91.

Eric W. Weisstein, MathWorld -- Waring's Problem.

Cf. A003325.

Table[Length[c = Table[j^3, {j, (10^n - 1)^(1/3)}];
  Select[Union[Flatten[Outer[Plus, c, c]]],
IntervalMemberQ[Interval[{10^(n - 1), 10^n - 1}], #] &]], {n, 10}] (* Robert Price, Apr 18 2019 *)

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

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

a(6)-a(11) from Charles R Greathouse IV, Oct 16 2013
a(12) from Lars Blomberg, Jan 15 2014
a(13)-a(17) from Hiroaki Yamanouchi, Jul 13 2014

A181378 Total number of n-digit numbers requiring 3 positive cubes in their representation as sum of cubes.

Original entry on oeis.org

1, 14, 107, 1006, 9550, 92743, 913905, 9060358, 90216532

Offset: 1

Martin Renner, Jan 28 2011

A181354(n) + A181376(n) + a(n) + A181380(n) + A181384(n) + A181401(n) + A181403(n) + A181405(n) + A171386(n) = A052268(n)

Eric W. Weisstein, MathWorld -- Waring's Problem.

Cf. A047702

a(n) = A181377(n)-A181377(n-1)

a(5)-a(9) from Lars Blomberg, Jan 15 2014

A181380 Total number of n-digit numbers requiring 4 positive cubes in their representation as sum of cubes.

Original entry on oeis.org

1, 17, 224, 3101, 43340, 558806, 6615757, 73663693, 784419159

Offset: 1

Martin Renner, Jan 28 2011

A181354(n) + A181376(n) + A181378(n) + a(n) + A181384(n) + A181401(n) + A181403(n) + A181405(n) + A171386(n) = A052268(n).

Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A047703, A181379.

Cf. A052268, A181354, A181376, A181378, A181384, A181401, A181403, A181405, A171386.

a(n) = A181379(n) - A181379(n-1).

a(5)-a(9) from Lars Blomberg, Jan 15 2014

A181384 Total number of n-digit numbers requiring 5 positive cubes in their representation as sum of cubes.

Original entry on oeis.org

1, 20, 272, 3549, 34234, 244503, 1454243, 7201405, 25018440

Offset: 1

Martin Renner, Jan 28 2011

A181354(n) + A181376(n) + A181378(n) + A181380(n) + a(n) + A181401(n) + A181403(n) + A181405(n) + A171386(n) = A052268(n)

Eric W. Weisstein, MathWorld -- Waring's Problem.

Cf. A047704

a(n) = A181381(n)-A181381(n-1)

a(5)-a(9) from Lars Blomberg, Jan 15 2014

A181403 Total number of n-digit numbers requiring 7 positive cubes in their representation as sum of cubes.

Original entry on oeis.org

1, 9, 63, 48

Offset: 1

Martin Renner, Jan 28 2011

A181354(n) + A181376(n) + A181378(n) + A181380(n) + A181384(n) + A181401(n) + a(n) + A181405(n) + A171386(n) = A052268(n).

Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A018890.

a(n) = A181402(n) - A181402(n-1).

A181405 Total number of n-digit numbers requiring 8 positive cubes in their representation as sum of cubes.

Original entry on oeis.org

0, 3, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Martin Renner, Jan 28 2011

Arthur Wieferich proved that only 15 integers require eight cubes, cf. A018889.

A181354(n) + A181376(n) + A181378(n) + A181380(n) + A181384(n) + A181401(n) + A181403(n) + a(n) + A171386(n) = A052268(n)

Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A018889, A181404.

a(n) = A181404(n) - A181404(n-1).

cp's OEIS Frontend

A181354 Number of n-digit perfect cubes.

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A171386 The characteristic function of 2 and 3: 1 if n is prime such that either n-1 or n+1 is prime, else 0.

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A181376 Total number of n-digit numbers requiring 2 positive cubes in their representation as a sum of cubes.

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A181378 Total number of n-digit numbers requiring 3 positive cubes in their representation as sum of cubes.

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A181380 Total number of n-digit numbers requiring 4 positive cubes in their representation as sum of cubes.

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A181384 Total number of n-digit numbers requiring 5 positive cubes in their representation as sum of cubes.

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A181403 Total number of n-digit numbers requiring 7 positive cubes in their representation as sum of cubes.

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A181405 Total number of n-digit numbers requiring 8 positive cubes in their representation as sum of cubes.

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