A098955 Numbers with property that the last digit is the length of the number (written in base 10).

1, 12, 22, 32, 42, 52, 62, 72, 82, 92, 103, 113, 123, 133, 143, 153, 163, 173, 183, 193, 203, 213, 223, 233, 243, 253, 263, 273, 283, 293, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 403, 413, 423, 433, 443, 453, 463, 473, 483, 493, 503

Offset: 1

Author

Eric Angelini, Oct 21 2004

Keywords

• base
• easy
• nonn
• fini

Comments

Otherwise said: list of n-digit numbers with n+1 appended, for n=0,1,2,... The sequence is obviously finite, since the largest possible digit and thus maximal possible length of a term is 9. The formula confirms that the last and largest term is a(10^8)=999999999. - M. F. Hasler, Jan 06 2013

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

1,seq(seq(10*(n-1)+d,n=10^(d-2)+1..10^(d-1)),d=2..4); # Robert Israel, Aug 17 2018

PARI

A098955(n)=n*10-9+#Str(n-1)-(n==1)  \\ M. F. Hasler, Jan 06 2013

Python

def a(n): s = str(n); return int(s + str(len(s) + int(n != 0)))
print([a(n) for n in range(51)]) # Michael S. Branicky, Aug 04 2022

Formula

a(n) = 10(n-1)+2 = 10n-8 for n=2,...,10,

a(n) = 10(n-1)+3 = 10n-7 for n=11,...,100,

a(n) = 10(n-1)+4 = 10n-6 for n=101,...,1000, and so on,

a(n) = 10(n-1)+k+1 = 10n-(9-k) for 10^(k-1) < n <= 10^k, up to

a(n) = 10(n-1)+9 = 10n-1 for n=10^7+1,...,10^8. - M. F. Hasler, Jan 06 2013