A078221 a(1) = 1, a(n+1) > a(n) is the smallest multiple of a(n) using only odd digits.

1, 3, 9, 99, 9999, 99999999, 9999999999999999, 99999999999999999999999999999999, 9999999999999999999999999999999999999999999999999999999999999999

Offset: 1

Author

Amarnath Murthy, Nov 22 2002

Keywords

• base
• nonn

Crossrefs

Cf. A078222.

Programs

Maple

1,3,seq(10^(2^(n-3))-1,n=3..11);

Python

def A078221(n): return 2*n-1 if n < 3 else 10**(2**(n-3)) - 1 # Chai Wah Wu, Jan 12 2022

Formula

a(n) = 10^(2^(n-3)) - 1 for n >= 3. (Proof by induction. Consider a(n)*f, L = ceiling(log(f)/log(10)), g1 = number formed by the first L digits of a(n)*f, g2 = number formed by the last L digits of a(n)*f => g1 + g2 = number formed by L 9's, if L <= 10^(2^(n-2)) + 1). - Sascha Kurz, Jan 04 2003

Extensions

More terms from Sascha Kurz, Jan 04 2003