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
Examples
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.
Links
Crossrefs
Cf. A316749.
Programs
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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
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