

A114802


3concatenationfree sequence starting (1,2).


0



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
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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 3Stöhr sequence with concatenation (base 10) substituting for addition. A026474 is a 3Stöhr sequence.


LINKS

Table of n, a(n) for n=1..59.
Eric Weisstein's World of Mathematics, Stöhr Sequence.


FORMULA

a(0) = 1, a(1) = 2, for n>2: a(n) = least k > a(n1) 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 *)


CROSSREFS

Cf. A084383, A033627, A026474.
Sequence in context: A180482 A193460 A114801 * A055933 A188650 A132578
Adjacent sequences: A114799 A114800 A114801 * A114803 A114804 A114805


KEYWORD

base,easy,nonn


AUTHOR

Jonathan Vos Post, Feb 18 2006


EXTENSIONS

Corrected and edited by Giovanni Resta, Jun 15 2016


STATUS

approved



