A346707 "Look once to the left" sequence, omitting a(k) for each iteration k, starting with 1,2 (see example).

1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2

Offset

1,2

Comments

The ratio of number of 2's to number of 1's appears to converge to 1.3985918...

Links

Table of n, a(n) for n=1..87.

Example

Begin with [1, 2].
Iteration 1: append to self, omitting term 1: [1, 2] + [2] = [1, 2, 2].
Iteration 2: append to self, omitting term 2: [1, 2, 2] + [1, 2] = [1, 2, 2, 1, 2].
Iteration 3: append to self, omitting term 3: [1, 2, 2, 1, 2] + [1, 2, 1, 2] = [1, 2, 2, 1, 2, 1, 2, 1, 2].

Mathematica

Block[{a = {1, 2}}, Do[a = Join[a, Delete[a, i]], {i, 7}]; a] (* Michael De Vlieger, Aug 04 2021 *)

Prog

(Python)
def sequence(iterations, start=[1, 2]):
  a = start
  for k in range(0, iterations):
    a = a + a[:k] + a[k+1:]
  return a
(PARI) a(n) = n-=2; while(n>0, my(k=logint(n, 2)); n-=1<<k; if(n<k, n--)); n+2; \\ Kevin Ryde, Aug 03 2021

Crossrefs

Cf. A000051, A293838.

Sequence in context: A319981 A052005 A377902 * A138702 A344339 A348364

Adjacent sequences: A346704 A346705 A346706 * A346708 A346709 A346710

Keyword

nonn

Author

Matthew Malone, Jul 29 2021

Status

approved