OFFSET
0,1
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + b(n-1)^9 - 9 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. - Seiichi Manyama, Aug 14 2019
EXAMPLE
9^9 == 9 (mod 10).
89^9 == 9 (mod 10^2).
289^9 == 9 (mod 10^3).
1289^9 == 9 (mod 10^4).
21289^9 == 9 (mod 10^5).
921289^9 == 9 (mod 10^6).
PROG
(PARI) n=0; for(i=1, 100, m=9; for(x=0, 9, if(((n+(x*10^(i-1)))^9)%(10^i)==m, n=n+(x*10^(i-1)); print1(x", "); break)))
(PARI) N=100; Vecrev(digits(lift(chinese(Mod((9+O(2^N))^(1/9), 2^N), Mod((9+O(5^N))^(1/9), 5^N)))), N) \\ Seiichi Manyama, Aug 06 2019
(Ruby)
def A225458(n)
ary = [9]
a = 9
n.times{|i|
b = (a + a ** 9 - 9) % (10 ** (i + 2))
ary << (b - a) / (10 ** (i + 1))
a = b
}
ary
end
p A225458(100) # Seiichi Manyama, Aug 14 2019
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Aswini Vaidyanathan, May 11 2013
STATUS
approved