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.

A113324 Inverse integer permutation of A113321.

Original entry on oeis.org

1, 2, 4, 3, 6, 5, 8, 10, 7, 12, 14, 9, 16, 11, 18, 20, 13, 22, 15, 24, 26, 17, 28, 30, 19, 32, 21, 34, 36, 23, 38, 40, 25, 42, 27, 44, 46, 29, 48, 31, 50, 52, 33, 54, 56, 35, 58, 37, 60, 62, 39, 64, 41, 66, 68, 43, 70, 72, 45, 74, 47, 76, 78, 49, 80, 82, 51, 84, 53, 86, 88, 55
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 26 2005

Keywords

Comments

A113325 = a(a(n));
a(n) = A113321(A113325(n)) = A113325(A113321(n)).

A113322 First differences of A113321.

Original entry on oeis.org

1, 2, -1, 3, -1, 4, -2, 5, -4, 6, -4, 7, -6, 8, -6, 9, -7, 10, -9, 11, -9, 12, -10, 13, -12, 14, -12, 15, -14, 16, -14, 17, -15, 18, -17, 19, -17, 20, -19, 21, -19, 22, -20, 23, -22, 24, -22, 25, -23, 26, -25, 27, -25, 28, -27, 29, -27, 30, -28, 31, -30, 32, -30, 33, -31, 34
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 26 2005

Keywords

Comments

a(n) = A113321(n+1) - A113321(n);
A000027 is a subsequence: a(A004277(n-1)) = n.

A113323 A113321(A113321(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 12, 9, 10, 7, 11, 8, 22, 14, 25, 17, 18, 19, 33, 13, 35, 15, 24, 16, 43, 27, 46, 30, 31, 20, 32, 21, 56, 23, 37, 38, 39, 40, 67, 26, 69, 28, 45, 29, 77, 48, 80, 51, 52, 53, 88, 34, 90, 36, 58, 59, 60, 61, 101, 64, 65, 41, 66, 42, 111, 44, 71, 72, 73, 74, 122
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 26 2005

Keywords

Comments

Inverse integer permutation of A113325;
A113324(a(n)) = a(A113324(n)) = A113321(n).

A244724 Lexicographically earliest permutation of the natural numbers such that primes and composites alternate in the sums of adjacent terms.

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jul 05 2014

Keywords

Comments

For k > 0: a(2*k-1) + a(2*k) is prime, a(2*k) + a(2*k+1) is composite.

Examples

			.             n | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
.          a(n) | 1 2 4 3 5 6 8 9 7 10 11 12 13 16 14 15 17 20 18 19
. A026233(a(n)) | 1 1 2 2 3 3 4 5 4  6  5  7  6 10  8  9  7 12 11  8 .
		

Crossrefs

Cf. A244732 (inverse), A244731 (fixed points), A073846, A113321, A115316.

Programs

  • Haskell
    import Data.List (delete)
    a244724 n = a244724_list !! (n-1)
    a244724_list = 1 : f 1 [2..] where
       f x xs = f' xs where
         f' (u:us) | a010051' (x + u) == 1 = g u (delete u xs)
                   | otherwise             = f' us where
            g y ys = g' ys where
              g' (v:vs) | a010051' (y + v) == 0 = u : v : f v (delete v ys)
                        | otherwise        = g' vs

Formula

A010051(a(n)+a(n+1)) = n mod 2.

A113325 A113324(A113324(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 10, 12, 8, 9, 11, 7, 20, 14, 22, 24, 16, 17, 18, 30, 32, 13, 34, 23, 15, 40, 26, 42, 44, 28, 29, 31, 19, 52, 21, 54, 35, 36, 37, 38, 62, 64, 25, 66, 43, 27, 72, 46, 74, 76, 48, 49, 50, 82, 84, 33, 86, 55, 56, 57, 58, 94, 96, 60, 61, 63, 39, 104, 41, 106, 67, 68
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 26 2005

Keywords

Comments

Inverse integer permutation of A113323;
A113321(a(n)) = a(A113321(n)) = A113324(n).
Showing 1-5 of 5 results.