A053654 Multiples of 123456789.

123456789, 246913578, 370370367, 493827156, 617283945, 740740734, 864197523, 987654312, 1111111101, 1234567890, 1358024679, 1481481468, 1604938257, 1728395046, 1851851835, 1975308624, 2098765413, 2222222202, 2345678991, 2469135780, 2592592569, 2716049358, 2839506147

Offset: 1

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 17 2000

Keywords

• easy
• nonn

References

• W. Lietzmann, Sonderlinge im Reich der Zahlen, Ferd. Duemmlers Verlag Bonn, 1948, p. 29.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Subsequence of A008591.

Programs

Mathematica

Array[123456789 # &, 19] (* Michael De Vlieger, May 15 2018 *)

PARI

a(n)=123456789*n \\ Charles R Greathouse IV, Jul 10 2016

Formula

a(n) = 2*a(n-1) - a(n-2). - Wesley Ivan Hurt, Apr 25 2023

From Elmo R. Oliveira, Jun 26 2025: (Start)

G.f.: 123456789*x/(1-x)^2.

E.g.f.: 123456789*x*exp(x).

a(n) = 123456789*n = 13717421*A008591(n). (End)