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.

A380183 Distinct nonnegative values of A380123, in order of appearance and with offset 0.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 15, 16, 13, 17, 14, 18, 19, 20, 21, 22, 24, 30, 32, 23, 31, 25, 33, 26, 34, 27, 28, 29, 35, 36, 37, 38, 40, 39, 41, 42, 43, 44, 47, 48, 59, 60, 63, 64, 45, 49, 61, 65, 46, 62, 50, 66, 51, 52, 67, 68, 53, 69, 54, 56, 55
Offset: 0

Views

Author

Rémy Sigrist, Jan 15 2025

Keywords

Comments

This sequence is a permutation of the nonnegative integers with inverse A380184.

Examples

			Sequence A380123 begins:     0, 0, 1, 0, 2, -1, 0, 3, 4, 0, 4, 0, 1, 4, 5, -2, 0, 6, 8.
The present sequence begins: 0,    1,    2,        3, 4,                5,        6, 8.
		

Crossrefs

Cf. A380123, A380184 (inverse), A380185.

Programs

  • PARI
    \\ See Links section.

A380185 Distinct nonpositive values of A380123, negated, in order of appearance and with offset 0.

Original entry on oeis.org

0, 1, 2, 5, 4, 3, 10, 8, 9, 7, 6, 21, 20, 17, 16, 19, 15, 18, 14, 13, 12, 11, 42, 40, 34, 32, 41, 33, 39, 31, 38, 30, 37, 36, 35, 29, 28, 27, 26, 24, 25, 23, 22, 85, 84, 81, 80, 69, 68, 65, 64, 83, 79, 67, 63, 82, 66, 78, 62, 77, 76, 61, 60, 75, 59, 74, 72, 73
Offset: 0

Views

Author

Rémy Sigrist, Jan 15 2025

Keywords

Comments

This sequence is a permutation of the nonnegative integers with inverse A380186.

Examples

			Sequence A380123 begins:     0, 0, 1, 0, 2, -1, 0, 3, 4, 0, 4, 0, 1, 4, 5, -2.
The present sequence begins: 0,              1,                             2.
		

Crossrefs

Cf. A380123, A380183, A380186 (inverse).

Programs

  • PARI
    \\ See Links section.

A380122 a(n) is the number of integers m (possibly negative) such that the nonzero digits in the nonadjacent form for m appear in the nonadjacent form for n.

Original entry on oeis.org

1, 2, 2, 4, 2, 4, 4, 4, 2, 4, 4, 8, 4, 8, 4, 4, 2, 4, 4, 8, 4, 8, 8, 8, 4, 8, 8, 8, 4, 8, 4, 4, 2, 4, 4, 8, 4, 8, 8, 8, 4, 8, 8, 16, 8, 16, 8, 8, 4, 8, 8, 16, 8, 16, 8, 8, 4, 8, 8, 8, 4, 8, 4, 4, 2, 4, 4, 8, 4, 8, 8, 8, 4, 8, 8, 16, 8, 16, 8, 8, 4, 8, 8, 16, 8
Offset: 0

Views

Author

Rémy Sigrist, Jan 12 2025

Keywords

Examples

			The nonadjacent form for 25 is "10T001" and has 3 nonzero digits, so a(25) = 2^3 = 8.
		

Crossrefs

Cf. A000120, A001316, A184617, A380123 (corresponding m's).

Programs

  • PARI
    a(n) = { my (v = 1); while (n, if (n%2, n -= 2 - (n%4); v *= 2; ); n \= 2; ); return (v); }

Formula

a(n) = 2^A000120(A184617(n)) = A001316(A184617(n)).

A380180 Irregular table T(n, k), n >= 0, k = 1..2^A005812(n); the n-th row lists the integers m (possibly negative) such that the nonzero digits in the balanced ternary expansion of m appear in the balanced ternary expansion of n.

Original entry on oeis.org

0, 0, 1, -1, 0, 2, 3, 0, 3, 0, 1, 3, 4, -4, -3, -1, 0, 5, 6, 8, 9, -3, 0, 6, 9, -3, -2, 0, 1, 6, 7, 9, 10, -1, 0, 8, 9, 0, 9, 0, 1, 9, 10, -1, 0, 2, 3, 8, 9, 11, 12, 0, 3, 9, 12, 0, 1, 3, 4, 9, 10, 12, 13, -13, -12, -10, -9, -4, -3, -1, 0, 14, 15, 17, 18, 23, 24, 26, 27
Offset: 0

Views

Author

Rémy Sigrist, Jan 15 2025

Keywords

Comments

Every integer appears infinitely many times in the sequence.
See A368239 (resp. A380181) for the nonnegative values (resp. the nonpositive values, negated) in order of appearance in the present sequence.

Examples

			Irregular table T(n, k) begins:
  n   n-th row
  --  -------------------------
   0  0
   1  0, 1
   2  -1, 0, 2, 3
   3  0, 3
   4  0, 1, 3, 4
   5  -4, -3, -1, 0, 5, 6, 8, 9
   6  -3, 0, 6, 9
   7  -3, -2, 0, 1, 6, 7, 9, 10
   8  -1, 0, 8, 9
   9  0, 9
  10  0, 1, 9, 10
  11  -1, 0, 2, 3, 8, 9, 11, 12
  12  0, 3, 9, 12
.
Irregular table T(n, k) begins in balanced ternary:
  n    n-th row
  ---  --------------------------------
    0  0
    1  0, 1
   1T  T, 0, 1T, 10
   10  0, 10
   11  0, 1, 10, 11
  1TT  TT, T0, T, 0, 1TT, 1T0, 10T, 100
  1T0  T0, 0, 1T0, 100
  1T1  T0, T1, 0, 1, 1T0, 1T1, 100, 101
  10T  T, 0, 10T, 100
  100  0, 100
  101  0, 1, 100, 101
  11T  T, 0, 1T, 10, 10T, 100, 11T, 110
  110  0, 10, 100, 110
		

Crossrefs

See A380123 for a similar sequence.

Programs

  • PARI
    row(n) = { my (r = [0], d, t = 1); while (n, d = centerlift(Mod(n, 3)); if (d, r = concat(r, [v + d*t | v <- r]);); n = (n-d)/3; t *= 3;); vecsort(r); }

Formula

T(n, 1) = - A060373(n).
T(n, 2^A005812(n)) = A060372(n).
Showing 1-4 of 4 results.