A217398 Numbers starting with 5.

5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542

Offset: 1

Author

Jeremy Gardiner, Oct 02 2012

Keywords

• nonn
• base
• easy

Comments

The lower and upper asymptotic densities of this sequence are 1/45 and 5/27, respectively. - Amiram Eldar, Feb 27 2021

Also numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 5. - Stefano Spezia, Jul 08 2025

Links

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

Crossrefs

Cf. A000867, A011535.

Subsequences include: A045711, A077330, A077681, A106415, A106425.

Cf. A131835, A217394, A217395, A217397, A217399, A217400, A217401, A217402.

Programs

Haskell

a217398 n = a217398_list !! (n-1)
a217398_list = filter ((== 5) . a000030) [1..]
-- Reinhard Zumkeller, Mar 13 2014

Mathematica

Select[Range[1000], IntegerDigits[#][[1]] == 5 &] (* T. D. Noe, Oct 02 2012 *)

Python

def A217398(n): return n+(44*10**(len(str(9*n-8))-1))//9 # Chai Wah Wu, Dec 07 2024

Formula

A000030(a(n)) = 5; A143473(a(n)) = a(n). - Reinhard Zumkeller, Mar 13 2014

a(n) = n + (44*10^floor(log_10(9*n-8))-8)/9. - Alan Michael Gómez Calderón, May 17 2023