

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



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



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



