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

1,2

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

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

Maple

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

Prog

(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

Crossrefs

Sequence in context: A278030 A286094 A348187 * A285470 A124885 A115745

Adjacent sequences: A098952 A098953 A098954 * A098956 A098957 A098958

Keyword

base,easy,nonn,fini

Author

Eric Angelini, Oct 21 2004

Status

approved