A169843 EKG sequence started at 6 instead of 2.

6, 2, 4, 8, 10, 5, 15, 3, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11, 33, 24, 26, 13, 39, 27, 30, 25, 35, 28, 32, 34, 17, 51, 36, 38, 19, 57, 42, 40, 44, 46, 23, 69, 45, 48, 50, 52, 54, 56, 49, 63, 60, 55, 65, 70, 58, 29, 87, 66, 62, 31, 93, 72, 64, 68, 74, 37, 111, 75, 78, 76, 80, 82, 41

Offset: 1

Author

T. D. Noe and N. J. A. Sloane, Jun 02 2010

Keywords

• nonn

Comments

A generalization of A064413.

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, EKG Sequence
• Index entries for sequences related to EKG sequence
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

For other initial terms, see A064413, A169837, A169839, A169841, A169845, A169847, A169849, A169851, A169853, A169855.

Programs

Mathematica

f[s_List] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]]; Nest[f, {6, 2}, 71] (* Michael De Vlieger, Jan 21 2016, after Robert G. Wilson v at A064413 *)

Python

from math import gcd
def aupton(terms):
  alst, aset = [1, 6], {1, 6}
  for n in range(2, terms+1):
    k = 2
    while True:
      while k in aset: k += 1
      if gcd(alst[-1], k) != 1: alst.append(k); aset.add(k); break
      k += 1
  return alst[1:]
print(aupton(73)) # Michael S. Branicky, Jun 02 2021