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

1,1

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.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A006092, A011533.

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

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

Sequence in context: A186681 A295430 A344430 * A077679 A045863 A121023

Adjacent sequences: A217392 A217393 A217394 * A217396 A217397 A217398

Keyword

nonn,base,easy

Author

Jeremy Gardiner, Oct 02 2012

Status

approved