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.
conc[x_, y_] := FromDigits@ Flatten@ IntegerDigits[{x, y}]; L = {1, 2}; cc = {12, 21}; Do[k = 1 + Max@L; While[MemberQ[cc, k], k++]; cc = Union[cc, conc[#, k] & /@ L, conc[k, #] & /@ L]; AppendTo[L, k];, {65}]; L (* Giovanni Resta, Jun 15 2016 *)
See Links section.
from itertools import count, islice
def agen(): # generator of terms
cats1, cats2, an, s = {"1", "2"}, {"12", "21"}, 3, "3"
yield from [1, 2]
while True:
yield an
cats2 |= {s + c for c in cats1} | {c + s for c in cats1}
cats1.add(s)
while (s:=str(an)) in cats1 or s in cats2:
an += 1
print(list(islice(agen(), 59))) # Michael S. Branicky, Feb 01 2024
conc[w_] := Flatten[ (FromDigits /@ Flatten /@ IntegerDigits /@ (Permutations[#]) &) /@ Subsets[w, {2, 3}]]; up = 10^3; L = {1, 2, 3}; cc = conc[L]; Do[k = 1 + Max@L; While[MemberQ[cc, k], k++]; If[k > up, Break[]]; Do[cc = Union[cc, Select[ conc[{k, L[[i]], L[[j]]}], # <= up &]], {i, Length[L]}, {j, i - 1}]; AppendTo[L, k], {60}]; L (* Giovanni Resta, Jun 15 2016 *)
from itertools import islice
def incats(s, L, k):
if s == "": return True
if k == 0: return False
return any(s.startswith(w) and incats(s[len(w):], L[:i]+L[i+1:], k-1) for i, w in enumerate(L))
def agen(): # generator of terms
L, an, s = ["1", "2"], 3, "3"
yield from [1, 2]
while True:
yield an
L.append(s)
while incats((s:=str(an)), L, 3):
an += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Feb 01 2024
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