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.

A116648 Least natural number which does not occur in A116626(1..n).

Original entry on oeis.org

2, 2, 4, 4, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 9, 9, 11, 11, 11, 11, 11, 11, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 27, 27, 27, 27, 27, 27, 27, 27, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 39, 39, 39, 39, 42, 42, 42, 42, 44, 44, 44, 44
Offset: 1

Views

Author

Antti Karttunen, Feb 21 2006

Keywords

Crossrefs

Cf. A116649, A116650, A116651.

A116627 a(n) = First integer i such that A116626(i) = n, 0 if n never occurs in A116626.

Original entry on oeis.org

1, 3, 2, 5, 9, 4, 15, 7, 17, 11, 23, 6, 8, 16, 10, 13, 19, 25, 29, 33, 41, 37, 14, 18, 24, 12, 49, 45, 53, 63, 57, 21, 27, 35, 31, 47, 59, 55, 67, 39, 43, 71, 22, 75, 79, 85, 89, 30, 20, 28, 26, 36, 44, 34, 32, 46, 56, 58, 54, 42, 40, 38, 48, 51, 61, 65, 73, 69, 81, 77, 95, 87
Offset: 1

Views

Author

Paul D. Hanna and Antti Karttunen, Feb 21 2006

Keywords

Comments

If A116626 is really a permutation of natural numbers, then this is as well and no zeros are needed.

Links

Crossrefs

Inverse: A116626.

A116624 a(1)=1; for n>1, a(n) = least positive integer not appearing earlier such that {a(k) | 1 <= k <= n} and {a(k) XOR a(k-1) | 1 <= k <= n} are disjoint sets of distinct numbers.

Original entry on oeis.org

1, 2, 4, 8, 5, 10, 16, 7, 9, 17, 32, 11, 18, 33, 19, 35, 20, 34, 22, 40, 21, 41, 28, 36, 27, 64, 29, 38, 31, 37, 65, 30, 66, 39, 68, 42, 67, 44, 70, 45, 69, 128, 46, 72, 47, 77, 129, 71, 131, 73, 130, 74, 132, 75, 134, 79, 136, 80, 133, 81, 135, 84, 137, 82, 139, 85
Offset: 1

Views

Author

Paul D. Hanna and Antti Karttunen, Feb 21 2006

Keywords

Comments

Another way to define this: A116624(1) = 1; A116624(n) = the least positive integer i distinct from any of A116624(1..n-1) and A116625(1..n-2), such that also (i XOR A116624(n-1)) is not present in A116625(1..n-2) nor in A116624(1..n-1).

Links

Crossrefs

Cf. Bisection of A116626. Complement of A116625?
Cf. A003987, A116624, A116628.
Cf. A235262

Programs

  • Mathematica
    a = {1}; used = {}; Do[k = 1; While[MemberQ[Join[a, used], k] || MemberQ[Join[a, used], r = BitXor[a[[-1]], k]], k++]; AppendTo[a, k]; AppendTo[used, r], {n, 2, 66}]; a (* Ivan Neretin, Mar 13 2017 *)

A116625 a(n) = A116624(n) XOR A116624(n+1).

Original entry on oeis.org

3, 6, 12, 13, 15, 26, 23, 14, 24, 49, 43, 25, 51, 50, 48, 55, 54, 52, 62, 61, 60, 53, 56, 63, 91, 93, 59, 57, 58, 100, 95, 92, 101, 99, 110, 105, 111, 106, 107, 104, 197, 174, 102, 103, 98, 204, 198, 196, 202, 203, 200, 206, 207, 205, 201, 199, 216, 213, 212
Offset: 1

Views

Author

Paul D. Hanna and Antti Karttunen, Feb 21 2006

Keywords

Comments

XOR is A003987.

Links

Crossrefs

Bisection of A116626. Complement of A116624?.
Cf. A235262.

A116649 Positions where A116648(i) is greater than A116648(i-1).

Original entry on oeis.org

1, 3, 5, 9, 15, 17, 23, 25, 29, 33, 41, 49, 53, 63, 67, 71, 75, 79, 85, 89, 95, 99, 103, 107, 139, 143, 163, 167, 175, 179, 199, 219, 223, 227, 235, 243, 267, 271, 275, 279, 283, 291, 299, 307, 323, 333, 337, 351, 357, 361, 371, 381, 395, 405, 425, 449, 457
Offset: 1

Views

Author

Antti Karttunen, Feb 21 2006

Keywords

Comments

Equivalently, from i>1 onward those i where A116626(i) = A116648(i-1). Conjecture: all the terms are odd.

Crossrefs

Cf. A116650.
Showing 1-5 of 5 results.

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