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

1,1

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.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A006092, A011532.

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

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

Sequence in context: A278938 A303157 A338994 * A072998 A024629 A235500

Adjacent sequences: A217391 A217392 A217393 * A217395 A217396 A217397

Keyword

nonn,base,easy

Author

Jeremy Gardiner, Oct 02 2012

Status

approved