A382441 Lexicographically earliest sequence of positive integers such that for any n > 1, a(n) does not divide any of the positive numbers whose decimal expansion appears as a contiguous subword in the concatenation of the previous terms.
1, 2, 5, 7, 8, 9, 10, 16, 20, 32, 40, 50, 51, 53, 64, 83, 93, 100, 117, 118, 126, 160, 186, 200, 207, 224, 250, 288, 311, 320, 352, 372, 391, 400, 448, 480, 500, 625, 640, 713, 800, 960, 979, 1000, 1011, 1039, 1043, 1097, 1099, 1173, 1200, 1250, 1359, 1426
Offset: 1
Examples
a(1) = 1. a(2) must not divide 1; we can take a(2) = 2. a(3) must not divide 1, 2 or 12; we can take a(3) = 5.
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..1000
- Rémy Sigrist, C++ program
Programs
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Python
from itertools import count, islice def agen(): # generator of terms an, s, d = 1, "1", [1] while True: yield an an = next(k for k in count(an+1) if not any(di%k == 0 for di in d)) for di in str(an): s += di d += [si for i in range(len(s)) if (si:=int(s[i:])) > an] d = sorted(set(d)) print(list(islice(agen(), 54))) # Michael S. Branicky, Mar 26 2025 (C++) // See Links section.
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