A217399 Numbers starting with 6.

6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642

Offset: 1

Author

Jeremy Gardiner, Oct 02 2012

Keywords

• nonn
• base
• easy

Comments

The lower and upper asymptotic densities of this sequence are 1/54 and 10/63, 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. A000870, A011536.

Subsequences include: A045712, A077331, A077682, A106416, A106426.

Cf. A131835, A217394, A217395, A217397, A217398, A217400, A217401, A217402.

Programs

GAP

Flat(List([0..2],n->List([0..10^n-1],k->6*10^n+k))); # Muniru A Asiru, Nov 21 2018

Magma

[n: n in [1..1600] | Intseq(n)[#Intseq(n)] eq 6]; // Vincenzo Librandi, Nov 24 2018

Maple

seq(seq(6*10^n+k, k=0..10^n-1),n=0..3); # Robert Israel, May 08 2017

Mathematica

Select[Range[1000], IntegerDigits[#][[1]] == 6 &] (* T. D. Noe, Oct 02 2012 *)

PARI

isok(n) = digits(n)[1] == 6; \\ Michel Marcus, May 08 2017

Python

def A217399(n): return n+(53*10**(len(str(9*n-8))-1))//9 # Chai Wah Wu, Dec 07 2024

Formula

a(n) = n + (53*10^floor(log_10(9*n-8))-8)/9. - Alan Michael Gómez Calderón, May 17 2023