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A070189 a(n) = 12345679*n.

%I A070189 #22 Jun 30 2025 21:44:38
%S A070189 0,12345679,24691358,37037037,49382716,61728395,74074074,86419753,
%T A070189 98765432,111111111,123456790,135802469,148148148,160493827,172839506,
%U A070189 185185185,197530864,209876543,222222222,234567901,246913580,259259259,271604938,283950617,296296296,308641975
%N A070189 a(n) = 12345679*n.
%C A070189 a(82)=1012345678 is the first term which has a digit appearing more than once without an obvious pattern, although a(-82)=-1012345678 might be seen as the concatenation of ten consecutive numbers.
%D A070189 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See entry 12345679 at p. 188.
%H A070189 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A070189 "TyYann", <a href="https://www.youtube.com/watch?v=P7Fbfu584ts">MegaFavNumbers: Lewis Carroll's Number</a>, video (2020).
%H A070189 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A070189 a(n) = n*(10^(10-1)-1)/(10-1)^2.
%F A070189 From _Elmo R. Oliveira_, Jun 26 2025: (Start)
%F A070189 G.f.: 12345679*x/(1-x)^2.
%F A070189 E.g.f.: 12345679*x*exp(x).
%F A070189 a(n) = 333667*A085959(n).
%F A070189 a(n) = 2*a(n-1) - a(n-2). (End)
%t A070189 Table[12345679*n,{n,0,30}] (* or *) LinearRecurrence[{2,-1},{0,12345679},30] (* _Harvey P. Dale_, Oct 16 2015 *)
%o A070189 (PARI) a(n)=12345679*n \\ _Charles R Greathouse IV_, Jan 09 2012
%o A070189 (PARI) concat(0, Vec(12345679*x/(1-x)^2 + O(x^26))) \\ _Elmo R. Oliveira_, Jun 26 2025
%Y A070189 Cf. A027889, A057932, A060073, A085959.
%K A070189 base,easy,nonn
%O A070189 0,2
%A A070189 _Henry Bottomley_, Apr 24 2002
%E A070189 More terms from _Elmo R. Oliveira_, Jun 26 2025