A387094 An infinite variant of the EKG sequence (A064413) such that for any n > 0, a(2*n) > a(2*n-1) and a(2*n) > a(2*n+1).

1, 4, 2, 6, 3, 12, 8, 10, 5, 15, 9, 18, 14, 20, 16, 22, 11, 33, 21, 27, 24, 26, 13, 39, 30, 32, 28, 34, 17, 51, 36, 38, 19, 57, 42, 44, 40, 45, 25, 35, 7, 56, 46, 50, 48, 54, 52, 58, 29, 87, 60, 62, 31, 93, 63, 66, 55, 70, 49, 84, 64, 72, 68, 74, 37, 111, 69

Offset: 1

Author

Rémy Sigrist, Aug 16 2025

Keywords

• nonn
• new

Comments

For the sequence to be infinite, when computing a term with even index, say a(2*n) for some n > 1, we must ensure that some missing value v < a(2*n) such that gcd(a(2*n), v) != 1 exists.

Will every integer appear in the sequence?

Examples

			Sequence begins:
  n   a(n)
  --  ----
   1     1
   2     4
   3     2
   4     6
   5     3
   6    12
   7     8
   8    10
   9     5
  10    15
  11     9
  12    18
  13    14
  14    20
  15    16
  16    22
  17    11
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10001
• Rémy Sigrist, PARI program
• Index entries for sequences related to EKG sequence

Crossrefs

Cf. A064413.

Programs

PARI

\\ See Links section.