A131835 Numbers starting with 1.

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142

Offset: 1

Author

Andrew Good (yipes_stripes(AT)yahoo.com), Jul 20 2007

Keywords

• nonn
• base
• easy

Comments

The lower and upper asymptotic densities of this sequence are 1/9 and 5/9, respectively. - Amiram Eldar, Feb 27 2021

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Bryan Brown, Michael Dairyko, Stephan Ramon Garcia, Bob Lutz and Michael Someck, Four quotient set gems, The American Mathematical Monthly, Vol. 121, No. 7 (2014), pp. 590-598; arXiv preprint, arXiv:1312.1036 [math.NT], 2013.
• Index entries for 10-automatic sequences.

Crossrefs

Subsequence of A011531.

Disjoint union of A045707 and A206286.

Cf. A000030, A000027, A002275, A262390 (permutation).

Cf. A217394, A217395, A217397, A217398, A217399, A217400, A217401, A217402.

Programs

Haskell

a131835 n = a131835_list !! (n-1)
a131835_list = concat $
               iterate (concatMap (\x -> map (+ 10 * x) [0..9])) [1]
-- Reinhard Zumkeller, Jul 16 2014

Maple

isA131835 := proc(n) if op(-1,convert(n,base,10)) = 1 then true; else false ; fi ; end: for n from 1 to 300 do if isA131835(n) then printf("%d, ",n) ; fi ; od : # R. J. Mathar, Jul 24 2007

Mathematica

Select[Range[150], IntegerDigits[#][[1]] == 1 &] (* Amiram Eldar, Feb 27 2021 *)

PARI

a(n, {base=10}) = my (o=1); while (n>o, n-=o; o*=base); return (o+n-1) \\ Rémy Sigrist, Jun 23 2017

PARI

a(n) = n--; s = #digits(9*n+1); n + 8 * (10^(s-1))/9 + 1/9 \\ David A. Corneth, Jun 23 2017

PARI

nxt(n) = my(d = digits(n+1)); if(d[1]==1, n+1, 10^#d) \\ David A. Corneth, Jun 23 2017

Python

def A131835(n): return n+(10**(len(str(9*n-8))-1)<<3)//9 # Chai Wah Wu, Dec 07 2024

Formula

A000030(a(n)) = 1. - Reinhard Zumkeller, Jul 16 2014

a(A002275(n)+1) = 10^n for any n >= 0. - Rémy Sigrist, Jun 23 2017

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

Extensions

More terms from R. J. Mathar, Jul 24 2007