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.

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A346795 Irregular triangle T(n, k), n > 0, k = 1..A091220(n), read by rows; the n-th row gives, in ascending order, the distinct integers k such that A048720(k, m) = n for some m.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 2, 4, 1, 3, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 3, 7, 9, 1, 2, 3, 5, 6, 10, 1, 11, 1, 2, 3, 4, 6, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 2, 4, 8, 16, 1, 3, 5, 15, 17, 1, 2, 3, 6, 7, 9, 14, 18, 1, 19, 1, 2, 3, 4, 5, 6, 10, 12, 20, 1, 7, 21
Offset: 1

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Author

Rémy Sigrist, Sep 29 2021

Keywords

Comments

The n-th row corresponds to the divisors of the n-th GF(2)[X]-polynomial.
The greatest value both in the n-th row and in the k-th row corresponds to A091255(n, k).
The index of the first row containing both n and k corresponds to A091256(n, k).

Examples

			The triangle starts:
      1:   [1]
      2:   [1, 2]
      3:   [1, 3]
      4:   [1, 2, 4]
      5:   [1, 3, 5]
      6:   [1, 2, 3, 6]
      7:   [1, 7]
      8:   [1, 2, 4, 8]
      9:   [1, 3, 7, 9]
     10:   [1, 2, 3, 5, 6, 10]
     11:   [1, 11]
     12:   [1, 2, 3, 4, 6, 12]
     13:   [1, 13]
     14:   [1, 2, 7, 14]
     15:   [1, 3, 5, 15]
		

Crossrefs

Programs

  • PARI
    See Links section.

Formula

T(n, 1) = 1.
T(n, A091220(n)) = n.
Sum_{k = 1..A091220(n)} T(n, k) = A280493(n).
T(n, 1) XOR ... XOR T(n, A091220(n)) = A178908(n) (where XOR denotes the bitwise XOR operator).
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