A217402 Numbers starting with 9.

9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942

Offset: 1

Author

Jeremy Gardiner, Oct 02 2012

Keywords

• nonn
• base
• easy

Comments

The lower and upper asymptotic densities of this sequence are 1/81 and 1/9, respectively. - Amiram Eldar, Feb 27 2021

Links

• Jeremy Gardiner, Table of n, a(n) for n = 1..1111
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A000981, A011539.

Subsequences include: A077685, A045715, A106419, A106429, A077334.

Cf. A131835, A217394, A217395, A217397, A217398, A217399, A217400, A217401.

Programs

Mathematica

Select[Range[1000], IntegerDigits[#][[1]] == 9 &] (* T. D. Noe, Oct 02 2012 *)

Python

def A217402(n): return n+(80*10**(len(str(9*n-8))-1))//9 # Chai Wah Wu, Dec 07 2024

Formula

a(n) = n + (80*10^floor(log_10(9*n-8))-8)/9. - Alan Michael Gómez Calderón, May 17 2023