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a(n+1) = concatenation of a(n) and a(n)+1, with a(0)=1.
3

%I #29 Oct 20 2021 21:29:40

%S 1,12,1213,12131214,1213121412131215,12131214121312151213121412131216,

%T 1213121412131215121312141213121612131214121312151213121412131217

%N a(n+1) = concatenation of a(n) and a(n)+1, with a(0)=1.

%C The next term is too large to be included in the DATA section. - _N. J. A. Sloane_, Oct 20 2021

%t NestList[FromDigits[Join[IntegerDigits[#],IntegerDigits[#+1]]]&,1,6] (* _Jayanta Basu_, May 20 2013 *)

%K nonn,base

%O 0,2

%A Wolfgang Scheufele (ws(AT)pi3.informatik.uni-mannheim.de)