A181354 -id:A181354 - cp's OEIS frontend

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.

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

A280640 Numbers k such that k^3 has an odd number of digits and the middle digit is 0.

Original entry on oeis.org

0, 30, 40, 42, 100, 101, 115, 116, 123, 126, 135, 163, 164, 171, 199, 200, 201, 214, 468, 479, 487, 498, 500, 502, 513, 520, 525, 543, 557, 562, 564, 575, 576, 577, 578, 579, 585, 596, 600, 615, 623, 642, 656, 661, 666, 690, 695, 697, 700, 705, 709, 717, 721

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 0, 27000, 64000, 74088, 1000000, 1030301, 1520875, 1560896, ...

			0^3 = (0), 126^3 = 200(0)376, 562^3 = 1775(0)4328.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280641-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

a[n_]:=Part[IntegerDigits[n], (Length[IntegerDigits[n]] + 1)/2];
Select[Range[0, 721], OddQ[Length[IntegerDigits[#^3]]] && a[#^3]==0 &] (* Indranil Ghosh, Mar 06 2017 *)

isok(k) = my(d=digits(k^3)); (#d%2 == 1) && (d[#d\2 +1] == 0);
for(k=0, 721, if(k==0 || isok(k)==1, print1(k, ", "))); \\ Indranil Ghosh, Mar 06 2017

i=0
j=1
while i<=721:
    n=str(i**3)
    l=len(n)
    if l%2 and n[(l-1)//2]=="0":
        print(str(i), end=",")
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

A280649 Numbers k such that k^3 has an odd number of digits and the middle digit is 9.

Original entry on oeis.org

28, 33, 41, 108, 132, 157, 159, 175, 178, 181, 184, 187, 190, 193, 196, 204, 207, 209, 466, 474, 480, 486, 492, 508, 514, 515, 518, 519, 528, 536, 539, 552, 570, 588, 611, 627, 638, 648, 651, 657, 658, 659, 660, 706, 707, 708, 714, 719, 745, 757, 763, 765, 772

Offset: 1

Lars Blomberg, Jan 07 2017

The sequence of cubes starts: 21952, 35937, 68921, 1259712, 2299968, 3869893, 4019679, 5359375, ...

			28^3 = 21(9)52, 181^3 = 592(9)741, 536^3 = 1539(9)0656.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Jeremy Gardiner, Middle digit in cube numbers, Seqfan Mailing list, Dec 12 2016.

Cf. A280640-A280648, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

ond9Q[n_]:=Module[{idn=IntegerDigits[n^3],len},len=Length[idn];OddQ[len]&&idn[[(len+1)/2]]==9]; Select[Range[800],ond9Q] (* Harvey P. Dale, Mar 14 2018 *)

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

A181401 Total number of n-digit numbers requiring 6 positive cubes in their representation as sum of cubes.

Original entry on oeis.org

1, 17, 184, 1123, 2115, 479, 3, 0, 0

Offset: 1

Martin Renner, Jan 28 2011

A181354(n) + A181376(n) + A181378(n) + A181380(n) + A181384(n) + a(n) + A181403(n) + A181405(n) + A171386(n) = A052268(n)

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

Cf. A046040

a(n) = A181400(n)-A181400(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

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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A280640 Numbers k such that k^3 has an odd number of digits and the middle digit is 0.

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A280649 Numbers k such that k^3 has an odd number of digits and the middle digit is 9.

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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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A181401 Total number of n-digit numbers requiring 6 positive cubes in their representation as sum of cubes.

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