

A114801


2concatenationfree 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
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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 2Stöhr sequence with concatenation (base 10) substituting for addition. A033627 "0additive sequence: not the sum of any previous pair" is another name for the 2Stöhr 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(n1) such that k is not an element of {Concatenate(a(i), a(j))} for any distinct a(i) <= a(n1) and a(j) <= a(n1).


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.


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



