cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 101-104 of 104 results.

A273123 Values of A007692(n) that are not of the form x^2 + y^2 + z^2 where x, y, z are nonzero integers.

Original entry on oeis.org

85, 130, 340, 520, 1360, 2080, 5440, 8320, 21760, 33280, 87040, 133120, 348160, 532480, 1392640, 2129920, 5570560, 8519680, 22282240, 34078720, 89128960, 136314880, 356515840, 545259520, 1426063360, 2181038080, 5704253440, 8724152320
Offset: 1

Views

Author

Altug Alkan, May 16 2016

Keywords

Comments

If n is in this sequence, then 4*n is also in this sequence. So 85*4^k and 130*4^k are terms of this sequence for all nonnegative values of k.
For more details see A051952.

Examples

			85 is a term because 85 = 2^2 + 9^2 = 6^2 + 7^2 and 85 = x^2 + y^2 + z^2 has no solution for nonzero integer values of x, y, z.
130 is a term because 130 = 3^2 + 11^2 = 7^2 + 9^2 and 130 = x^2 + y^2 + z^2 has no solution for nonzero integer values of x, y, z.
340 is a term because 340 = 4*85 and 85 is a term.

Crossrefs

Cf. A000408, A004214, A007692, A051952.

Programs

  • Mathematica
    twoQ[n_] := 2 == Length@ Select[ PowersRepresentations[n, 2, 2], Times @@ # > 0 &, 2]; threeQ[n_] := {} != Quiet@ IntegerPartitions[n, {3}, Range[ Sqrt@ n]^2, 1]; Select[Range[10^5], twoQ[#] && ! threeQ[#] &] (* Giovanni Resta, May 16 2016 *)

Extensions

a(14)-a(28) from Giovanni Resta, May 16 2016

A273843 Numbers that are the average of 3 nonzero squares and the average of 2 positive cubes.

Original entry on oeis.org

1, 8, 14, 27, 36, 63, 64, 76, 112, 140, 172, 185, 216, 234, 260, 288, 343, 364, 378, 427, 504, 512, 536, 608, 666, 679, 728, 729, 868, 896, 972, 1000, 1030, 1099, 1112, 1120, 1161, 1270, 1331, 1376, 1404, 1463, 1480, 1628, 1688, 1728, 1750, 1764, 1859, 2052, 2080, 2156
Offset: 1

Views

Author

Altug Alkan, Jun 01 2016

Keywords

Comments

Values of (x^3 + y^3)/2 such that (x^3 + y^3)/2 = (a^2 + b^2 + c^2)/3 where x, y, a, b, c > 0, is soluble.

Examples

			14 is a term because 14 = (1^3 + 3^3)/2 = (1^2 + 4^2 + 5^2)/3.

Crossrefs

Cf. A000408, A003325, A267702.

Programs

  • Mathematica
    repQ[n_,k_,e_] := {} != Quiet@ IntegerPartitions[n, {k}, Range[n^ (1/e) ]^e, 1]; Select[Range@ 2156, repQ[2*#,2,3] && repQ[3*#,3,2] &] (* Giovanni Resta, Jun 03 2016 *)
  • PARI
    isA000408(n) = my(a, b) ; a=1 ; while(a^2+1A003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
lista(nn) = for(n=1, nn, if(isA003325(2*n) && isA000408(3*n), print1(n, ", ")));

A274255 Numbers n such that n^2 is the sum of three nonzero squares while n is not.

Original entry on oeis.org

7, 13, 15, 23, 25, 28, 31, 37, 39, 47, 52, 55, 58, 60, 63, 71, 79, 85, 87, 92, 95, 100, 103, 111, 112, 119, 124, 127, 130, 135, 143, 148, 151, 156, 159, 167, 175, 183, 188, 191, 199, 207, 208, 215, 220, 223, 231, 232, 239, 240, 247, 252, 255, 263, 271, 279, 284
Offset: 1

Views

Author

Altug Alkan, Jun 16 2016

Keywords

Examples

			7 is a term because 7 is not in A000408 and 7^2 = 49 = 2^2 + 3^2 + 6^2.

Crossrefs

Cf. A000408, A005767.

Programs

  • PARI
    isA000408(n) = my(a, b) ; a=1 ; while(a^2+1A000408(n) && isA000408(n^2), print1(n, ", ")));

A329063 a(n) = a(n-1)! + a(n-1) with a(1)=1.

Original entry on oeis.org

1, 2, 4, 28, 304888344611713860501504000028
Offset: 1

Views

Author

Ananthakrishna Kaithalayil, Nov 02 2019

Keywords

Comments

The next term is too large to include, since it has about 8.85695956*10^30 digits.
No term can be represented by a sum of three positive squares, because a(4) and the following terms can all be written as 4*(8*k+7) for k>=0.

Examples

			a(3) = a(3-1)! + a(3-1) = a(2)! + a(2) = 4.

Crossrefs

Cf. A000408 (sums of 3 squares).

Programs

  • Mathematica
    a[1]=1; a[n_] := a[n-1]! + a[n-1]; Array[a, 5] (* Giovanni Resta, Nov 03 2019 *)

Formula

a(n) = a(n-1)! + a(n-1)

Extensions

Edited by N. J. A. Sloane, Nov 03 2019
Previous Showing 101-104 of 104 results.

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