A070189 a(n) = 12345679*n.

0, 12345679, 24691358, 37037037, 49382716, 61728395, 74074074, 86419753, 98765432, 111111111, 123456790, 135802469, 148148148, 160493827, 172839506, 185185185, 197530864, 209876543, 222222222, 234567901, 246913580, 259259259, 271604938, 283950617, 296296296, 308641975

Offset: 0

Author

Henry Bottomley, Apr 24 2002

Keywords

• base
• easy
• nonn

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).

Crossrefs

Cf. A027889, A057932, A060073, A085959.

Programs

Mathematica

Table[12345679*n,{n,0,30}] (* or *) LinearRecurrence[{2,-1},{0,12345679},30] (* Harvey P. Dale, Oct 16 2015 *)

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

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)

Extensions

More terms from Elmo R. Oliveira, Jun 26 2025