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 1-2 of 2 results.

A256399 First differences of A256219.

Original entry on oeis.org

1, 1, 3, 1, 3, 3, 1, 3, 8, 3, 5, 4, 3, 1, 4, 10, 1, 4, 4, 4, 4, 7, 4, 9, 3, 1, 4, 3, 4, 16, 4, 4, 4, 8, 1, 8, 7, 1, 8, 4, 4, 8, 3, 4, 4, 8, 16, 1, 3, 1, 11, 1, 4, 12, 7, 5, 3, 1, 8, 3, 5, 19, 4, 1, 3, 16, 5, 11, 1, 4, 4, 11, 5, 7
Offset: 1

Views

Author

N. J. A. Sloane, Mar 28 2015

Keywords

Links

Crossrefs

Cf. A121216, A256219.

A121216 a(1)=1, a(2) = 2; thereafter a(n) = the smallest positive integer which does not occur earlier in the sequence and which is coprime to a(n-2).

Original entry on oeis.org

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

Views

Author

Leroy Quet, Aug 20 2006

Keywords

Comments

Permutation of the positive natural numbers with inverse A225047: a(A225047(n)) = A225047(a(n)) = n. - Reinhard Zumkeller, Apr 25 2013
I confirm that this is a permutation. - N. J. A. Sloane, Mar 28 2015 [This can be proved using an argument similar to (but simpler than) the proof in A093714. - N. J. A. Sloane, May 05 2022]

Links

Crossrefs

Cf. A084937, A121217, A225047, A098550, A256219 (positions of primes), A256399.
See also A352933, A352934, A352935, A352936, A352937, A353705, A353707, A353708.

Programs

  • Haskell
    import Data.List (delete, (\\))
a121216 n = a121216_list !! (n-1)
a121216_list = 1 : 2 : f 1 2 [3..] where
f x y zs = g zs where
  g (u:us) = if gcd x u == 1 then h $ delete u zs else g us where
   h (v:vs) = if gcd y v == 1 then u : v : f u v (zs \\ [u,v]) else h vs
-- Reinhard Zumkeller, Apr 25 2013
  • Mathematica
    Nest[Append[#, Block[{k = 3}, While[Nand[FreeQ[#, k], GCD[#[[-2]], k] == 1], k++]; k]] &, {1, 2}, 70] (* Michael De Vlieger, Dec 26 2019 *)

Extensions

Extended by Ray Chandler, Aug 22 2006
Showing 1-2 of 2 results.

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

Content is available under The OEIS End-User License Agreement.