A217395 Numbers starting with 3.

3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342

Offset: 1

Author

Jeremy Gardiner, Oct 02 2012

Keywords

• nonn
• base
• easy

Comments

The lower and upper asymptotic densities of this sequence are 1/27 and 5/18, 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, A011533.

Subsequences include: A045709, A077328, A077679, A106413, A106423.

Cf. A131835, A217394, A217397, A217398, A217399, A217400, A217401, A217402.

Programs

Mathematica

Select[Range[1000], IntegerDigits[#][[1]] == 3 &] (* T. D. Noe, Oct 02 2012 *)

PARI

a(n) = n + 26*10^logint(9*n,10)\9; \\ Kevin Ryde, Mar 30 2021

Python

def agen():
  yield 3
  digits, adder = 1, 30
  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, Mar 30 2021

Python

def A217395(n): return n+26*10**(len(str(9*n-8))-1)//9 # Chai Wah Wu, Sep 11 2024

Formula

a(n) = n + (26*10^floor(log_10(9*n-8))-8)/9. - Alan Michael Gómez Calderón, May 16 2023