OFFSET
0,2
COMMENTS
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.
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See entry 12345679 at p. 188.
LINKS
Tanya Khovanova, Recursive Sequences.
"TyYann", MegaFavNumbers: Lewis Carroll's Number, video (2020).
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(n) = n*(10^(10-1)-1)/(10-1)^2.
From Elmo R. Oliveira, Jun 26 2025: (Start)
G.f.: 12345679*x/(1-x)^2.
E.g.f.: 12345679*x*exp(x).
a(n) = 333667*A085959(n).
a(n) = 2*a(n-1) - a(n-2). (End)
MATHEMATICA
Table[12345679*n, {n, 0, 30}] (* or *) LinearRecurrence[{2, -1}, {0, 12345679}, 30] (* Harvey P. Dale, Oct 16 2015 *)
PROG
(PARI) a(n)=12345679*n \\ Charles R Greathouse IV, Jan 09 2012
(PARI) concat(0, Vec(12345679*x/(1-x)^2 + O(x^26))) \\ Elmo R. Oliveira, Jun 26 2025
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Henry Bottomley, Apr 24 2002
EXTENSIONS
More terms from Elmo R. Oliveira, Jun 26 2025
STATUS
approved