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 1-5 of 5 results.

A341194 a(n) is the least k such that A340873(k) = n.

Original entry on oeis.org

1, 2, 4, 3, 6, 12, 5, 10, 20, 13, 25, 9, 17, 34, 29, 57, 114, 41, 81, 49, 97, 33, 65, 129, 113, 225, 449, 169, 337, 201, 401, 801, 285, 545, 489, 925, 1833, 641, 1281, 769, 1537, 513, 1025, 2049, 1793, 3585, 1473, 2689, 1665, 3201, 6401, 2557, 4381, 3753, 7505
Offset: 0

Views

Author

Rémy Sigrist, Feb 06 2021

Keywords

Examples

			See Illustration in Links section.
		

Crossrefs

Programs

  • C
    See Links section.

Formula

a(n) <= 2^n.
a(n+1) <= 2*a(n).

A341218 a(n) is the number of numbers k such that A340873(k) = n.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 6, 8, 11, 15, 21, 29, 40, 54, 74, 102, 139, 189, 259, 355, 486, 664, 908, 1242, 1697, 2317, 3165, 4326, 5911, 8076, 11034, 15073, 20588, 28125, 38415, 52477, 71692, 97931, 133774, 182739, 249634, 341013, 465839, 636346, 869279, 1187486
Offset: 0

Views

Author

Rémy Sigrist, Feb 07 2021

Keywords

Examples

			The first terms, alongside the correspond k's, are:
   n  a(n)  k's
   -  ----  ----------------------
   0     1              1
                        |
   1     1              2
                        |
   2     1              4
                       / \
   3     2            3   8
                     /   / \
   4     3          6   7   16
                   /   /   /  \
   5     4       12  14  15    32
		

Crossrefs

Programs

  • PARI
    See Links section.

Formula

a(n) <= a(n+1) <= 2*a(n).

A341220 Irregular table read by rows T(n, k), n >= 0, k = 1..A341218(n); T(n, k) is the k-th number m such that A340873(m) = n.

Original entry on oeis.org

1, 2, 4, 3, 8, 6, 7, 16, 12, 14, 15, 32, 5, 24, 28, 30, 31, 64, 10, 11, 48, 56, 60, 62, 63, 128, 20, 21, 22, 23, 96, 112, 120, 124, 126, 127, 256, 13, 40, 42, 43, 44, 46, 47, 192, 224, 240, 248, 252, 254, 255, 512, 25, 26, 27, 80, 84, 85, 86, 87, 88, 92, 94, 95, 384, 448, 480, 496, 504, 508, 510, 511, 1024
Offset: 0

Views

Author

Rémy Sigrist, Feb 07 2021

Keywords

Comments

Each positive integer appears once.
For any n >= 0:
- if m appears in row n, then 2*m appears in row n+1,
- if m appears in row n and is an odious even number > 2, then an additional odd number appears in row n+1.

Examples

			Table begins:
    1;
    2;
    4;
    3, 8;
    6, 7, 16;
    12, 14, 15, 32;
    5, 24, 28, 30, 31, 64;
    10, 11, 48, 56, 60, 62, 63, 128;
    20, 21, 22, 23, 96, 112, 120, 124, 126, 127, 256;
    13, 40, 42, 43, 44, 46, 47, 192, 224, 240, 248, 252, 254, 255, 512;
    ...
		

Crossrefs

Programs

  • PARI
    See Links section.

Formula

T(n, 1) = A341194(n).
T(n, A341218(n)) = 2^n.

A341231 Irregular triangle read by rows giving trajectory from n to reach 1 under the map A245471.

Original entry on oeis.org

1, 2, 1, 3, 4, 2, 1, 4, 2, 1, 5, 14, 7, 8, 4, 2, 1, 6, 3, 4, 2, 1, 7, 8, 4, 2, 1, 8, 4, 2, 1, 9, 26, 13, 22, 11, 28, 14, 7, 8, 4, 2, 1, 10, 5, 14, 7, 8, 4, 2, 1, 11, 28, 14, 7, 8, 4, 2, 1, 12, 6, 3, 4, 2, 1, 13, 22, 11, 28, 14, 7, 8, 4, 2, 1, 14, 7, 8, 4, 2, 1
Offset: 1

Views

Author

Rémy Sigrist, Feb 07 2021

Keywords

Comments

A340873 gives row lengths.
A341235 gives greatest terms.

Examples

			Table begins:
    1;
    2, 1;
    3, 4, 2, 1;
    4, 2, 1;
    5, 14, 7, 8, 4, 2, 1;
    6, 3, 4, 2, 1;
    7, 8, 4, 2, 1;
    8, 4, 2, 1;
    9, 26, 13, 22, 11, 28, 14, 7, 8, 4, 2, 1;
    10, 5, 14, 7, 8, 4, 2, 1;
    11, 28, 14, 7, 8, 4, 2, 1;
    12, 6, 3, 4, 2, 1;
    13, 22, 11, 28, 14, 7, 8, 4, 2, 1;
    14, 7, 8, 4, 2, 1;
    15, 16, 8, 4, 2, 1;
    16, 8, 4, 2, 1;
    ...
		

Crossrefs

Programs

  • PARI
    row(n) = { my (r=[n]); while (n>1, r=concat(r, n=if (n%2, bitxor(n, 2*n+1), n/2))); r }

Formula

T(n, 1) = n.
T(n, A340873(n)) = 1.

A341235 a(n) is the greatest term in n-th row of A341231.

Original entry on oeis.org

1, 2, 4, 4, 14, 6, 8, 8, 28, 14, 28, 12, 28, 14, 16, 16, 62, 28, 52, 20, 62, 28, 56, 24, 62, 28, 44, 28, 52, 30, 32, 32, 122, 62, 100, 36, 110, 52, 104, 40, 122, 62, 124, 44, 118, 56, 112, 48, 122, 62, 84, 52, 112, 54, 88, 56, 110, 58, 76, 60, 100, 62, 64, 64
Offset: 1

Views

Author

Rémy Sigrist, Feb 07 2021

Keywords

Comments

Records of a(n)/n appear to happen for n in A083318.

Examples

			For n = 10:
- the trajectory of 10 under A245471 is 10 -> 5 -> 14 -> 7 -> 8 -> 4 -> 2 -> 1,
- so a(10) = 14.
		

Crossrefs

Programs

  • PARI
    a(n) = { my (m=n); while (n>1, m=max(m, n=if (n%2, bitxor(n, 2*n+1), n/2))); m }

Formula

a(n) >= n, equality implies that n equals 1 or is even.
a(n) < 4*n.
Showing 1-5 of 5 results.