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a(n) = 12345679*n.
2

%I #19 Sep 18 2024 16:32:50

%S 0,12345679,24691358,37037037,49382716,61728395,74074074,86419753,

%T 98765432,111111111,123456790,135802469,148148148,160493827,172839506,

%U 185185185,197530864,209876543,222222222,234567901,246913580,259259259

%N a(n) = 12345679*n.

%C 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 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See entry 12345679 at p. 188.

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.

%H "TyYann", <a href="https://www.youtube.com/watch?v=P7Fbfu584ts">MegaFavNumbers: Lewis Carroll's Number</a>, video (2020).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = n*(10^(10-1)-1)/(10-1)^2.

%t Table[12345679*n,{n,0,30}] (* or *) LinearRecurrence[{2,-1},{0,12345679},30] (* _Harvey P. Dale_, Oct 16 2015 *)

%o (PARI) a(n)=12345679*n \\ _Charles R Greathouse IV_, Jan 09 2012

%Y Cf. A027889, A057932, A060073.

%K base,easy,nonn

%O 0,2

%A _Henry Bottomley_, Apr 24 2002