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A098406
a(n) = (10^n + 17)/9.
4
2, 3, 13, 113, 1113, 11113, 111113, 1111113, 11111113, 111111113, 1111111113, 11111111113, 111111111113, 1111111111113, 11111111111113, 111111111111113, 1111111111111113, 11111111111111113, 111111111111111113, 1111111111111111113, 11111111111111111113, 111111111111111111113
OFFSET
0,1
COMMENTS
A097683 gives numbers k such that a(k) is prime.
FORMULA
a(1) = 3; a(n) = a(n-1) + 10^(n-1).
a(1) = 3; a(n) = 10*a(n-1) - 17.
a(n) = A047855(n)+1 = A002275(n)+2.
G.f.: (2-19*x)/((10*x-1)*(x-1)). - R. J. Mathar, Jan 27 2017
From Elmo R. Oliveira, Aug 23 2024: (Start)
E.g.f.: exp(x)*(exp(9*x) + 17)/9.
a(n) = A062397(n) - A002282(n).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1. (End)
EXAMPLE
a(5) = (100000 + 17)/9 = 11113.
MATHEMATICA
FromDigits/@Table[PadLeft[{3}, n, 1], {n, 20}] (* Harvey P. Dale, Jun 18 2011 *)
PROG
(PARI) for(n=1, 18, print1(((10^n)+17)/9, ", "))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Sep 07 2004
EXTENSIONS
a(0) from Ivan Panchenko, Nov 02 2013
STATUS
approved