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.
Quiet[Block[{$ContextPath}, Needs["Combinatorica`"]], {General::compat}]
theta = E;
sums = {0};
cached = <||>;
A023123[i_] := Module[{term, path, base},
While[sums[[-1]] < i,
term = sums[[-1]] + Floor[theta * (Length[sums] - 1)] + 1;
AppendTo[sums, term];
cached[term] = 1
];
path = {i};
While[Not[KeyExistsQ[cached, path[[-1]]]],
AppendTo[path, path[[-1]] - Combinatorica`BinarySearch[sums, path[[-1]]] + 3/2];
];
base = cached[path[[-1]]];
MapIndexed[(cached[#1] = base + Length[path] - First[#2]) &, path];
cached[i]
];
Print[Table[A023123[i], {i, 1, 100}]]; (* Brady J. Garvin, Sep 13 2024 *)
from bisect import bisect
from sympy import floor, E
theta = E
sums = [0]
cached = {}
def A023123(i):
while sums[-1] < i:
term = sums[-1] + floor(theta * (len(sums) - 1)) + 1
sums.append(term)
cached[term] = 1
path = [i]
while path[-1] not in cached:
path.append(path[-1] - bisect(sums, path[-1]) + 1)
base = cached[path[-1]]
for offset, vertex in enumerate(reversed(path)):
cached[vertex] = base + offset
return cached[i]
print([A023123(i) for i in range(1, 1001)]) # Brady J. Garvin, Sep 13 2024
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