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.

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A276345 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = A055938(a(n)), a(A088359(n)) = A005187(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

Original entry on oeis.org

1, 2, 3, 5, 4, 7, 6, 12, 10, 8, 15, 9, 11, 14, 13, 27, 23, 19, 16, 31, 21, 18, 22, 17, 26, 30, 20, 25, 24, 29, 28, 58, 53, 46, 38, 32, 63, 48, 41, 35, 42, 40, 34, 50, 33, 57, 62, 44, 39, 49, 37, 47, 45, 36, 56, 55, 61, 43, 54, 52, 51, 60, 59, 121, 113, 104, 89, 74, 64, 127, 108, 95, 81, 70, 82, 93, 79, 67, 98, 77, 66, 112, 65, 120
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276346.
Cf. A004001, A005187, A055938, A080677, A087686, A088359, A093879.
Similar or related permutations: A233276, A233278, A267111, A276343, A276441.

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A055938(a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A005187(1+a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A233276(A276441(n)).
a(n) = A233278(A267111(n)).

A276443 Permutation of natural numbers: a(1) = 1, a(A087686(n)) = A000069(1+a(n-1)), a(A088359(n)) = A001969(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001, and A000069 & A001969 are odious & evil numbers.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 11, 15, 13, 14, 16, 17, 18, 20, 24, 19, 23, 30, 21, 27, 25, 22, 29, 31, 26, 28, 32, 33, 34, 36, 40, 48, 35, 39, 46, 60, 37, 43, 54, 41, 51, 49, 38, 45, 58, 47, 63, 61, 42, 53, 55, 50, 44, 57, 59, 62, 52, 56, 64, 65, 66, 68, 72, 80, 96, 67, 71, 78, 92, 120, 69, 75, 86, 108, 73, 83, 102, 81
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276444.
Cf. A000069, A001969, A004001, A080677, A087686, A088359, A093879.
Similar or related permutations: A003188, A276441, A276445 (compare the scatter plots).

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A000069(1+a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A001969(1+a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A003188(A276441(n)).

A120474 Second differences of A004001.

Original entry on oeis.org

1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, -1, 0, 0, 1, 0, 0, 0, -1, 1, 0, -1, 1, -1, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 0, 0, 1
Offset: 1

Views

Author

Roger L. Bagula, Jul 06 2006

Keywords

Comments

Takes values in {0,1,-1}.

Links

Crossrefs

Cf. A004001. First differences of A093879.

Programs

  • Mathematica
    Differences[#, 2] &@ Nest[Append[#1, #1[[#1[[-1]] ]] + #1[[#2 - #1[[-1]] ]] ] & @@ {#, Length@ # + 1} &, {1, 1}, 105] (* Michael De Vlieger, Nov 05 2018 *)

Formula

a(n) = A004001(n+2) - 2*A004001(n+1) + A004001(n) = A093879(n+1) - A093879(n).

Extensions

Edited by N. J. A. Sloane, Oct 01 2006

A269851 a(0) = 1, a(A087686(1+n)) = 2*a(n), a(A088359(n)) = A250469(a(n)), where A088359 and A087686 = numbers that occur only once (resp. more than once) in A004001.

Original entry on oeis.org

1, 2, 4, 3, 8, 9, 5, 6, 16, 21, 25, 7, 18, 15, 10, 12, 32, 45, 55, 49, 11, 42, 51, 35, 50, 27, 14, 36, 33, 30, 20, 24, 64, 93, 115, 91, 121, 13, 90, 123, 125, 77, 110, 147, 65, 98, 39, 22, 84, 105, 85, 102, 87, 70, 100, 57, 54, 28, 72, 69, 66, 60, 40, 48, 128, 189, 235, 203, 187, 169, 17, 186, 267, 305, 217, 143, 230
Offset: 0

Views

Author

Antti Karttunen, Mar 07 2016

Keywords

Comments

Permutation of natural numbers obtained from the sieve of Eratosthenes, combined with the permutation obtained from Hofstadter-Conway $10000 sequence (A004001). Note the indexing: Domain starts from 0, range from 1.

Links

Crossrefs

Inverse: A269852.
Cf. A004001, A087686, A088359, A093879, A250469.
Related or similar permutations: A252755, A267111, A269855.

Formula

a(0) = 1, a(1) = 2, for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = 2*a(n - A004001(n)), otherwise [when n is in A088359], a(n) = A250469(a(A004001(n)-1)).
As a composition of related permutations:
a(n) = A252755(A267111(n)).
Other identities. For all n >= 0:
a(2^n) = 2^(n+1).

A317015 a(n) = n for n < 2, a(n) = a(freq(a(n-1),n)) + a(freq(a(n-2),n)) for n >= 2, where freq(i, j) is the number of times i appears in the first j terms.

Original entry on oeis.org

0, 1, 2, 2, 4, 3, 2, 3, 4, 4, 4, 8, 5, 2, 5, 6, 3, 3, 8, 6, 4, 5, 5, 8, 6, 4, 4, 6, 7, 5, 4, 7, 6, 5, 5, 6, 5, 6, 7, 5, 6, 8, 8, 6, 7, 8, 6, 6, 16, 9, 2, 4, 7, 7, 4, 6, 9, 7, 5, 7, 8, 7, 7, 8, 8, 8, 8, 16, 10, 3, 4, 11, 9, 3, 4, 7, 13, 9, 5, 12, 9, 4, 5, 7, 10, 7, 4, 7, 10, 7, 8, 11, 7, 5, 5, 10, 9
Offset: 0

Views

Author

Altug Alkan, Jul 19 2018

Keywords

Comments

Inspired by A316774.
Let b(n) = n for n < 3, b(n) = b(freq(b(n-1),n)) for n >= 3, where freq(i, j) is the number of times i appears in the first j terms and b(n) has offset 0. For n >= 1, b(n) - 1 are 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, ... (cf. A093879). While b(n) has one parent spot, this entry (a(n)) has two parent spots which are freq(a(n-1),n) and freq(a(n-2),n).

Links

Crossrefs

Cf. A316774.

Programs

  • Maple
    b:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= `if`(n<2, n, a(b(a(n-1)))+a(b(a(n-2))));
      b(t):= b(t)+1; t
    end:
seq(a(n), n=0..200);  # Alois P. Heinz, Jul 19 2018
  • Mathematica
    Nest[Append[#, #[[Count[#, #[[-1]] ] + 1]] + #[[Count[#, #[[-2]] ] + 1 ]] ] &, {0, 1}, 95] (* Michael De Vlieger, Jul 20 2018 *)
Previous Showing 11-15 of 15 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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