A217394 Numbers starting with 2.

2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242

Offset: 1

Author

Jeremy Gardiner, Oct 02 2012

Keywords

• nonn
• base
• easy

Comments

The lower and upper asymptotic densities of this sequence are 1/18 and 10/27, 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. A006092, A011532.

Subsequences include: A045708, A045726, A077327, A077678, A106412, A106422.

Cf. A131835, A217395, A217397, A217398, A217399, A217400, A217401, A217402.

Programs

Mathematica

Select[Range[300], IntegerDigits[#][[1]] == 2 &] (* T. D. Noe, Oct 02 2012 *)

Python

def agen():
  yield 2
  digits, adder = 1, 20
  while True:
    for i in range(10**digits): yield adder + i
    digits, adder = digits+1, adder*10
g = agen()
print([next(g) for i in range(54)]) # Michael S. Branicky, Feb 20 2021

Python

def A217394(n): return n+(17*10**(len(str(9*n-8))-1))//9 # Chai Wah Wu, Dec 07 2024

Formula

a(n) = n + (17*10^floor(log_10(9*n-8))-8)/9. - Alan Michael Gómez Calderón, May 15 2023