A339853 Read one digit d at the time, starting from the first one; extend S with the smallest multiple of d not yet present in the sequence. Zeros are not read.

1, 2, 4, 8, 16, 3, 6, 9, 12, 18, 5, 10, 7, 24, 15, 11, 14, 20, 28, 13, 25, 17, 19, 21, 32, 22, 26, 40, 23, 27, 30, 35, 29, 42, 31, 36, 34, 33, 39, 38, 44, 46, 48, 54, 52, 50, 45, 56, 49, 51, 57, 55, 58, 63, 60, 62, 66, 37, 69, 72, 75, 64, 78, 81, 84, 90, 87, 80, 68, 76, 88, 96, 92, 104, 65, 100, 70, 74, 85, 108

Offset

1,2

Comments

This is a permutation of the integers > 0 (as the prime numbers are multiples of 1).

Links

Carole Dubois, Table of n, a(n) for n = 1..5000

Index entries for sequences that are permutations of the natural numbers

Example

The first d is 1; as 1 is already in the sequence, we extend it with 2;
the next d is now 2; as 2 is already in the sequence, we extend it with 4 (smallest multiple of 2 not in the sequence);
the next d is 4; as 4 is already in the sequence, we extend it with 8 (smallest multiple);
the next d is 8; as 8 is already in the sequence, we extend it with 16 (smallest multiple);
the next d is 1; we extend the sequence with 3 as 3 is the smallest multiple of 1 not yet present in the sequence;
the next d is 6; as 6 is not yet present, we extend the sequence with 6;
the next d is 3; we extend the sequence with 9 as 9 is the smallest multiple of 3 not yet present;
the next d is 6; we extend the sequence with 12 as 12 is the smallest multiple of 6 not yet present; etc.
As the zero of 10 will not be read, we will extend the sequence at that point with the smallest multiple of 7 not yet present -- which is 14.

Prog

(Python)
def aupto(n):
  alst, astr, used, strind = [1], "1", {1}, 0
  for k in range(1, n):
    while astr[strind] == "0": strind += 1
    ak = digit = int(astr[strind])
    while ak in used: ak += digit
    alst.append(ak); astr += str(ak); used.add(ak); strind += 1
  return alst    # use alst[n-1] for a(n)
print(aupto(71)) # Michael S. Branicky, Dec 19 2020

Crossrefs

Cf. A316749.

Sequence in context: A247292 A069783 A102251 * A373944 A218338 A218468

Adjacent sequences: A339850 A339851 A339852 * A339854 A339855 A339856

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Dec 19 2020

Status

approved