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 A114802 3-concatenation-free sequence starting (1,2). 1
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 121, 131, 141, 151, 161, 171, 181, 191, 200, 212, 232, 242, 252, 262, 272, 282, 292, 300, 313, 323, 343, 353, 363, 373, 383, 393, 400, 414, 424, 434, 454 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Starting with the terms (1,2) this sequence consists of minimum increasing integer terms such that no term is the concatenation of any two or three previous distinct terms. The next consecutive numbers skipped after 121 are 122 = Concatenate(1,22) and 123 = Concatenate(1,2,3). This is the analog of a 3-Stöhr sequence with concatenation (base 10) substituting for addition. A026474 is a 3-Stöhr sequence. LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Stöhr Sequence. FORMULA a(0) = 1, a(1) = 2, for n>2: a(n) = least k > a(n-1) such that k is not an element of {Concatenate[a(h),a(i),a(j)]} or {Concatenate[a(i),a(j)]} for any three distinct a(h), a(i), and a(j), where h, i, j < n. MATHEMATICA 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 *) PROG (Python) 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 CROSSREFS Cf. A084383, A033627, A026474. Sequence in context: A180482 A193460 A114801 * A055933 A188650 A132578 Adjacent sequences: A114799 A114800 A114801 * A114803 A114804 A114805 KEYWORD base,nonn AUTHOR Jonathan Vos Post, Feb 18 2006 EXTENSIONS Corrected and edited by Giovanni Resta, Jun 15 2016 STATUS approved

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Last modified August 8 03:17 EDT 2024. Contains 375018 sequences. (Running on oeis4.)