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 1-4 of 4 results.

A368226 Inverse permutation to A368225.

Original entry on oeis.org

0, 1, 3, 2, 4, 10, 8, 11, 6, 5, 7, 12, 9, 13, 33, 29, 34, 25, 23, 26, 35, 30, 36, 19, 17, 20, 15, 14, 16, 21, 18, 22, 37, 31, 38, 27, 24, 28, 39, 32, 40, 106, 98, 107, 90, 86, 91, 108, 99, 109, 78, 74, 79, 70, 68, 71, 80, 75, 81, 110, 100, 111, 92, 87, 93, 112
Offset: 0

Views

Author

Rémy Sigrist, Dec 18 2023

Keywords

Examples

			A368225(42) = 80, so a(80) = 42.
		

Crossrefs

Cf. A368225.

Programs

  • PARI
    See Links section.

A368229 Irregular table of nonnegative integers T(n, k), n >= 0, k = 1..A001316(n), read by rows: the 1's in the binary expansion of n exactly match the nonzero digits in the ternary expansions of the terms in the n-th row.

Original entry on oeis.org

0, 1, 2, 3, 6, 4, 5, 7, 8, 9, 18, 10, 11, 19, 20, 12, 15, 21, 24, 13, 14, 16, 17, 22, 23, 25, 26, 27, 54, 28, 29, 55, 56, 30, 33, 57, 60, 31, 32, 34, 35, 58, 59, 61, 62, 36, 45, 63, 72, 37, 38, 46, 47, 64, 65, 73, 74, 39, 42, 48, 51, 66, 69, 75, 78
Offset: 0

Views

Author

Rémy Sigrist, Dec 18 2023

Keywords

Comments

As a flat sequence, this is a permutation of the nonnegative integers (with inverse A368230).

Examples

			Table T(n, k) begins:
    0;
    1, 2;
    3, 6;
    4, 5, 7, 8;
    9, 18;
    10, 11, 19, 20;
    12, 15, 21, 24;
    13, 14, 16, 17, 22, 23, 25, 26;
    27, 54;
    28, 29, 55, 56;
    30, 33, 57, 60;
    31, 32, 34, 35, 58, 59, 61, 62;
    36, 45, 63, 72;
    37, 38, 46, 47, 64, 65, 73, 74;
    39, 42, 48, 51, 66, 69, 75, 78;
    40, 41, 43, 44, 49, 50, 52, 53, 67, 68, 70, 71, 76, 77, 79, 80;
    81, 162;
    ...
		

Crossrefs

See A368225 for a similar sequence.

Programs

  • PARI
    row(n) = { my (r = [0], b = binary(n)); for (k = 1, #b, r = [3*v+b[k]|v<-r]; if (b[k], r = concat(r, [v+1|v<-r]););); Set(r); }

Formula

T(n, 1) = A005836(n + 1).
T(n, A001316(n)) = A005823(n + 1).
A289831(T(n, k)) = n.

A368239 Irregular table of nonnegative integers T(n, k), n >= 0, k = 1..A080100(n), read by rows; the 1's in the binary expansion of n exactly match the 1's in the balanced ternary expansions of the terms in the n-th row.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 7, 10, 11, 12, 13, 14, 15, 17, 18, 23, 24, 26, 27, 16, 19, 25, 28, 20, 21, 29, 30, 22, 31, 32, 33, 35, 36, 34, 37, 38, 39, 40, 41, 42, 44, 45, 50, 51, 53, 54, 68, 69, 71, 72, 77, 78, 80, 81, 43, 46, 52, 55, 70, 73, 79, 82, 47, 48, 56, 57, 74, 75, 83, 84
Offset: 0

Views

Author

Rémy Sigrist, Dec 18 2023

Keywords

Comments

As a flat sequence, this is a permutation of the nonnegative integers with inverse A368240.

Examples

			Table T(n, k) begins:
    0;
    1;
    2, 3;
    4;
    5, 6, 8, 9;
    7, 10;
    11, 12;
    13;
    14, 15, 17, 18, 23, 24, 26, 27;
    16, 19, 25, 28;
    20, 21, 29, 30;
    22, 31;
    32, 33, 35, 36;
    34, 37;
    38, 39;
    40;
    ...
		

Crossrefs

See A368225 for a similar sequence.

Programs

  • PARI
    row(n) = { my (r = [0], b = binary(n)); for (k = 1, #b, r = [3*v+b[k]|v<-r]; if (b[k]==0, r = concat(r, [v-1|v<-r]););); Set(r); }

Formula

T(n, 1) = A147991(n) for any n > 0.
T(n, A080100(n)) = A005836(n + 1).
A343228(T(n, k)) = n.

A379175 Irregular triangle T(n, k), n >= 0, k = 1..ceiling(2^(A007895(n)-1)); the n-th row lists the nonnegative integers m such that A184617(m) = A003714(n).

Original entry on oeis.org

0, 1, 2, 4, 3, 5, 8, 7, 9, 6, 10, 16, 15, 17, 14, 18, 12, 20, 11, 13, 19, 21, 32, 31, 33, 30, 34, 28, 36, 27, 29, 35, 37, 24, 40, 23, 25, 39, 41, 22, 26, 38, 42, 64, 63, 65, 62, 66, 60, 68, 59, 61, 67, 69, 56, 72, 55, 57, 71, 73, 54, 58, 70, 74, 48, 80, 47, 49, 79, 81
Offset: 0

Views

Author

Rémy Sigrist, Dec 17 2024

Keywords

Comments

Also the nonnegative terms of A379147, in order of appearance.
This sequence is a permutation of the nonnegative integers with inverse A379176.
This sequence shares graphical features with A368225.

Examples

			Triangle T(n, k) begins:
  n   n-th row
  --  --------------
   0  0
   1  1
   2  2
   3  4
   4  3, 5
   5  8
   6  7, 9
   7  6, 10
   8  16
   9  15, 17
  10  14, 18
  11  12, 20
  12  11, 13, 19, 21
  13  32
  14  31, 33
  15  30, 34
		

Crossrefs

Programs

  • PARI
    tozeck(n) = { for (i=0, oo, if (n<=fibonacci(2+i), my (v=0, f); forstep (j=i, 0, -1, if (n>=f=fibonacci(2+j), n-=f; v+=2^j;); if (n==0, return (v););););); }
    row(n) = { my (z = tozeck(n), r = [0], b); while (z, z -= b = 2^valuation(z, 2); r = concat([v - b | v <- r], [v + b | v <- r]);); return (select(v -> v >= 0, r)); }

Formula

T(n, ceiling(2^(A007895(n)-1))) = A003714(n).
Showing 1-4 of 4 results.