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.
51 is a term because the first three multiples of 51 (51, 102, 153) all contain the digit 1, and 51 is the least positive integer with this property.
3 is a term because the first three multiples of 51 (51, 102, 153) all contain the decimal digit 1, and this is the unique longest sequence of this kind whose first term is 51 or less.
a(2)=37 since 37 and 74 contain a 7.
Table[SelectFirst[Range[10^6], Times @@ Boole@ Map[DigitCount[#, 10, 7] > 0 &, # Range@ n] > 0 &], {n, 12}] (* Michael De Vlieger, Apr 27 2017, Version 10 *)
a(3)=624 since 624, 1248, and 1872 all contain a 2.
a(2)=153 since 153 and 306 both contain a 3, and 153 is the smallest number for which this is the case.
from itertools import count, islice
def agen(startn=1, startk=1):
n = startn
for k in count(startk):
ki, nn = k, 0
while "3" in str(ki): ki += k; nn += 1
while n < ki//k: yield k; n += 1
print(list(islice(agen(), 22))) # Michael S. Branicky, Jul 31 2022
a(3) = 47 since 47, 94 and 141 all contain a 4.
def aupton(terms):
k, n, alst = 1, 1, []
while len(alst) < terms:
while not all(str(i*k).count('4') > 0 for i in range(1, n+1)): k += 1
while str(n*k).count('4') > 0: alst.append(k); n += 1
k += 1
return alst[:terms]
print(aupton(39)) # Michael S. Branicky, Apr 24 2021
a(3)=25 since 25, 50, and 75 all contain a 5.
a(2)=63 since 63 and 126 contain a 6.
a(2)=84 since 84 and 168 contain a 8.
a(11)=99 since 99, 198, 297, 396, 495, 594, 693, 792, 891, 990, and 1089 all contain a 9.
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