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.

Showing 1-3 of 3 results.

A364887 Inverse permutation to A364884.

Original entry on oeis.org

1, 2, 4, 3, 7, 5, 11, 6, 10, 8, 16, 9, 22, 12, 14, 13, 29, 15, 37, 17, 19, 23, 46, 18, 28, 30, 25, 24, 56, 20, 67, 21, 32, 38, 35, 26, 79, 47, 40, 27, 92, 33, 106, 31, 43, 57, 121, 34, 66, 36, 49, 39, 137, 41, 52, 42, 59, 68, 154, 44, 172, 80, 55, 48, 62, 50
Offset: 1

Views

Author

Rémy Sigrist, Aug 12 2023

Keywords

Examples

			A364884(42) = 56, hence a(56) = 42.

Links

Crossrefs

Cf. A364884.

Programs

  • PARI
    See Links section.

A364885 Triangle T(n, k), n >= 0, k = 0..n, read by rows; T(0, 0) = 0, and for any n > 0, k = 0..n, T(n, k) is the least number obtained by turning a 0 into a 1 in the binary expansion of the k-th term of the (0-based) flattened sequence.

Original entry on oeis.org

0, 1, 3, 2, 5, 7, 4, 9, 11, 6, 8, 17, 19, 10, 13, 16, 33, 35, 18, 21, 15, 32, 65, 67, 34, 37, 23, 12, 64, 129, 131, 66, 69, 39, 20, 25, 128, 257, 259, 130, 133, 71, 36, 41, 27, 256, 513, 515, 258, 261, 135, 68, 73, 43, 14, 512, 1025, 1027, 514, 517, 263, 132, 137, 75, 22, 24
Offset: 0

Views

Author

Rémy Sigrist, Aug 12 2023

Keywords

Comments

In other words, T(n, k) = a(k) OR 2^e for some e >= 0 (where OR denotes the bitwise OR operator).
As a flat sequence, this is a permutation of the nonnegative integers (as, for any h >= 0, the sequence contains all numbers with Hamming weight h); see A365080 for the inverse.

Examples

			Triangle begins:
    0
    1, 3
    2, 5, 7
    4, 9, 11, 6
    8, 17, 19, 10, 13
    16, 33, 35, 18, 21, 15
    32, 65, 67, 34, 37, 23, 12
    64, 129, 131, 66, 69, 39, 20, 25
    128, 257, 259, 130, 133, 71, 36, 41, 27
    256, 513, 515, 258, 261, 135, 68, 73, 43, 14
    512, 1025, 1027, 514, 517, 263, 132, 137, 75, 22, 24
    ...

Links

Crossrefs

See A364884 for a similar sequence.
Cf. A000120, A057945, A365080 (inverse).

Programs

  • PARI
    See Links section.

Formula

T(n, 0) = 2^(n-1) for any n > 0.
A000120(a(n)) = A057945(n).

A365230 Triangle T(n, k), n > 0, k = 1..n, read by rows and filled the greedy way with distinct positive integers such that T(n, k) is a multiple of T(k, 1).

Original entry on oeis.org

1, 2, 4, 3, 6, 9, 5, 8, 12, 10, 7, 14, 15, 20, 21, 11, 16, 18, 25, 28, 22, 13, 24, 27, 30, 35, 33, 26, 17, 32, 36, 40, 42, 44, 39, 34, 19, 38, 45, 50, 49, 55, 52, 51, 57, 23, 46, 48, 60, 56, 66, 65, 68, 76, 69, 29, 54, 63, 70, 77, 88, 78, 85, 95, 92, 58
Offset: 1

Views

Author

Rémy Sigrist, Aug 27 2023

Keywords

Comments

As a flat sequence, this is a permutation of the positive integers (as each row starts with the least value not yet in the sequence); see A365231 for the inverse.

Examples

			Triangle T(n, k) begins:
         1;
         2,  4;
         3,  6,  9;
         5,  8, 12, 10;
         7, 14, 15, 20, 21;
        11, 16, 18, 25, 28, 22;
        13, 24, 27, 30, 35, 33, 26;
        17, 32, 36, 40, 42, 44, 39, 34;
        19, 38, 45, 50, 49, 55, 52, 51, 57;
        ...................................
T(k, 1)  1   2   3   5   7  11  13  17  19

Links

Crossrefs

See A364884 and A365232 for similar sequences.
Cf. A365231 (inverse).

Programs

  • PARI
    See Links section.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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