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 A114801 2-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, 123, 124, 125, 126, 127, 128, 129, 131, 132, 134, 135, 136, 137, 138, 139, 141, 142, 143, 145, 146, 147, 148, 149, 151, 152, 153, 154, 156, 157, 158 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Starting with the terms (1,2) this sequence consists of minimum increasing terms such that no term is the concatenation of any two previous distinct terms. The next consecutive number skipped after 121 is 122 = Concatenate(1, 22). This is the analog of a 2-Stöhr sequence with concatenation (base 10) substituting for addition. A033627 "0-additive sequence: not the sum of any previous pair" is another name for the 2-Stöhr sequence. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Stöhr Sequence. Rémy Sigrist, PARI program for A114801 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(i), a(j))} for any distinct a(i) <= a(n-1) and a(j) <= a(n-1). MATHEMATICA 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 *) PROG (PARI) See Links section. (Python) 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 CROSSREFS Cf. A084383, A033627. Sequence in context: A125289 A180482 A193460 * A114802 A055933 A188650 Adjacent sequences: A114798 A114799 A114800 * A114802 A114803 A114804 KEYWORD base,easy,nonn AUTHOR Jonathan Vos Post, Feb 18 2006 EXTENSIONS Data corrected by Giovanni Resta, Jun 14 2016 STATUS approved

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Last modified September 19 13:45 EDT 2024. Contains 376012 sequences. (Running on oeis4.)