A064417 a(1) = 1, a(2) = 2, a(3) = 3; for n >3 a(n) = smallest number not already used such that gcd(a(n), a(n-1)) >= 3.

1, 2, 3, 6, 9, 12, 4, 8, 16, 20, 5, 10, 15, 18, 21, 7, 14, 28, 24, 27, 30, 25, 35, 40, 32, 36, 33, 11, 22, 44, 48, 39, 13, 26, 52, 56, 42, 45, 50, 55, 60, 51, 17, 34, 68, 64, 72, 54, 57, 19, 38, 76, 80, 65, 70, 49, 63, 66, 69, 23, 46, 92, 84, 75, 78, 81, 87, 29, 58, 116, 88, 77, 91

Offset: 1

Author

Jonathan Ayres (Jonathan.ayres(AT)btinternet.com), Sep 30 2001

Keywords

• nonn
• nice
• easy

Comments

A permutation of the natural numbers.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, arXiv:math/0204011 [math.NT], 2002; Exper. Math. 11 (2002), 437-446.
• J. C. Lagarias, E. M. Rains and N. J. A. Sloane, Problem 10927, Amer. Math. Monthly, 109 (2002), 202; The EKG Sequence: 10927, 111 (No. 2, 2004), 167-168.
• Index entries for sequences related to EKG sequence
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A064413. A064956 gives inverse permutation.

Programs

Haskell

import Data.List (delete)
a064417 n = a064417_list !! (n-1)
a064417_list = 1 : 2 : 3 : f 3 [4..] where
   f x us = x' : f x' (delete x' us) where
      x' = head [u | u <- us, gcd u x > 2]
-- Reinhard Zumkeller, Nov 13 2011

Mathematica

a[n_ /; n <= 3] := n; a[n_] := a[n] = For[aa = Array[a, n-1] // Sort; k = If[n == 4, 4, Complement[Range[aa // Last], aa] // First]; aa = Drop[aa, k-1], True, k++, If[FreeQ[aa, k], If[GCD[k, a[n-1]] >= 3, Return[k]]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 28 2015 *)

Extensions

More terms from Naohiro Nomoto, Sep 30 2001