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.

A084469 Position of A084467(n) in A084468(n).

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 5, 8, 9, 12, 10, 11, 15, 16, 13, 18, 14, 17, 20, 23, 21, 22, 19, 24, 26, 31, 27, 30, 28, 29, 25, 32, 33, 40, 34, 39, 35, 38, 36, 37, 45, 46, 41, 50, 42, 49, 43, 48, 44, 47, 54, 57, 55, 56, 51, 60, 52, 59, 53, 58, 64, 69, 65, 68, 66, 67, 61, 72, 62, 71, 63, 70
Offset: 1

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Antti Karttunen, Jun 02 2003

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Inverse permutation: A084470.

A084470 Position of A084468(n) in A084467(n).

Original entry on oeis.org

1, 2, 3, 4, 7, 5, 6, 8, 9, 11, 12, 10, 15, 17, 13, 14, 18, 16, 23, 19, 21, 22, 20, 24, 31, 25, 27, 29, 30, 28, 26, 32, 33, 35, 37, 39, 40, 38, 36, 34, 43, 45, 47, 49, 41, 42, 50, 48, 46, 44, 55, 57, 59, 51, 53, 54, 52, 60, 58, 56, 67, 69, 71, 61, 63, 65, 66, 64, 62, 72, 70, 68
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

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Inverse permutation: A084469.

A084468 Odd numbers with exactly 3 ones in binary expansion.

Original entry on oeis.org

7, 11, 13, 19, 21, 25, 35, 37, 41, 49, 67, 69, 73, 81, 97, 131, 133, 137, 145, 161, 193, 259, 261, 265, 273, 289, 321, 385, 515, 517, 521, 529, 545, 577, 641, 769, 1027, 1029, 1033, 1041, 1057, 1089, 1153, 1281, 1537, 2051, 2053, 2057, 2065, 2081, 2113, 2177
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

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Intersection of A005408 and A014311.
A084470(n) gives the position of a(n) in A084467(n).
Cf. A018900.

Programs

  • Mathematica
    Flatten[Table[2^m + 2^n + 1, {m, 2, 11}, {n, m - 1}]] (* Alonso del Arte, Jul 08 2011 *)
  • PARI
    for(m=2, 9, for(n=1, m-1, print1(2^m+2^n+1", "))) \\ Charles R Greathouse IV, Oct 04 2011
  • Python
    from math import isqrt, comb
def A084468(n): return (1<<(m:=isqrt(n<<3)+1>>1)+1)+(1<<(n-comb(m,2)))|1 # Chai Wah Wu, Apr 07 2025

Formula

a(n) = 2*A018900(n) + 1 = A005408(A018900(n)).
Sum_{n>=1} 1/a(n) = 0.714295772926319061998427422200268976390844375453066534198594764887682975019... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022

A084457 Juggling states associated with the juggling sequence A084458.

Original entry on oeis.org

7, 11, 13, 38, 19, 25, 140, 70, 35, 21, 74, 37, 82, 41, 276, 138, 69, 98, 49, 536, 268, 134, 67, 97, 2096, 1048, 524, 262, 131, 73, 548, 274, 137, 324, 162, 81, 1064, 532, 266, 133, 322, 161, 4176, 2088, 1044, 522, 261, 386, 193, 8288, 4144, 2072, 1036, 518, 259, 145
Offset: 0

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Author

Antti Karttunen, Jun 02 2003

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Same sequence in binary: A084456.
Terms that are odd: A084467.

Formula

a(0)=7, a(n) = (A084457(n-1) + 2^A084458(n) - 1)/2.

A084464 Positions of odd juggling states in A084457, i.e., positions of nonzero-throws in A084458 - 1.

Original entry on oeis.org

0, 1, 2, 4, 5, 8, 9, 11, 13, 16, 18, 22, 23, 28, 29, 32, 35, 39, 41, 46, 48, 54, 55, 59, 62, 67, 70, 76, 78, 85, 86, 90, 94, 99, 103, 109, 112, 119, 121, 129, 130, 139, 140, 145, 150, 156, 160, 167, 170, 178, 180, 189, 191, 201, 202, 208, 213, 220, 224, 232, 235, 244
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

Keywords

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Complement: A084463. Used to compute A084467.
Showing 1-5 of 5 results.

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