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.
a(2) = 86 as the iterations are : 1 -> 2 -> 4 -> 8 -> 16 -> 32 -> 64 -> 128 -> 256 -> 512 -> 1024 -> 2048 -> 4096 -> 8192 -> 16384 -> 32768 -> 65536 -> 6536 -> 13072 -> 26144 -> 2614 -> 5228 -> 528 -> 1056 -> 2112 -> 212 -> 424 -> 848 -> 1696 -> 3392 -> 392 -> 784 -> 1568 -> 3136 -> 6272 -> 12544 -> 1254 -> 2508 -> 5016 -> 10032 -> 1032 -> 2064 -> 4128 -> 8256 -> 16512 -> 33024 -> 3024 -> 6048 -> 12096 -> 24192 -> 48384 -> 96768 -> 193536 -> 387072 -> 774144 -> 7414 -> 14828 -> 29656 -> 59312 -> 118624 -> 18624 -> 37248 -> 74496 -> 7496 -> 14992 -> 1492 -> 2984 -> 5968 -> 11936 -> 1936 -> 3872 -> 7744 -> 74 -> 148 -> 296 -> 592 -> 1184 -> 184 -> 368 -> 736 -> 1472 -> 2944 -> 294 -> 588 -> 58 -> 116 -> 16, taking 86 steps to reach a repeated value. a(10) = 3 as the iterations are : 1 -> 10 -> 100 -> 10, taking three steps to reach a repeated value. a(11) = 2 as the iterations are : 1 -> 11 -> 1, taking two steps to reach a repeated value.
from itertools import groupby
def a(n):
seen, k, c = set(), 1, 0
while k not in seen:
seen.add(k)
c += 1
s = str(k)
t = "".join(k for k, g in groupby(s))
k = k*n if s == t else int(t)
return c
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Jan 11 2024
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