This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
A308539(33) = 42, hence a(42) = 33.
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The first terms are: n a(n) a(n)/A30(n) | n a(n) a(n)/A30(n) -- ---- ----------- | -- ---- ----------- 1 1 1 | 16 16 16 2 2 1 | 17 17 17 3 3 1 | 18 18 18 4 4 1 | 19 19 19 5 5 1 | 20 20 10 6 6 1 | 21 22 11 7 7 1 | 22 24 12 8 8 1 | 23 26 13 9 9 1 | 24 28 14 10 10 10 | 25 30 15 11 11 11 | 26 32 16 12 12 12 | 27 34 17 13 13 13 | 28 36 18 14 14 14 | 29 38 19 15 15 15 | 30 21 7
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from itertools import count, islice
def agen(): # generator of terms
aset, m = set(), 1
for n in count(1):
n1 = int(str(n)[0])
an = next(k for k in count(m) if k not in aset and k%n1 == 0)
yield an
aset.add(an)
while m in aset: m += 1
print(list(islice(agen(), 67))) # Michael S. Branicky, Jan 27 2025
The initial digit of a(1) = 1 is 1 and 1 divides a(2) = 2; The initial digit of a(2) = 2 is 2 and 2 divides a(4) = 4; The initial digit of a(3) = 3 is 3 and 3 divides a(6) = 6; etc.
from itertools import count from math import lcm a = list(range(10)) while len(a) <= 100: a.append(next(k*m for k in count() if k*(m:=lcm(*[d for i in range(len(a)-9,len(a)) if (d:= int(str(a[i])[0]))+i == len(a)])) not in a)) print(a[1:]) # Dominic McCarty, Mar 12 2025
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