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

1,2

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.

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

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 *)

Prog

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

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.

Sequence in context: A169905 A076161 A318699 * A262390 A102236 A250040

Adjacent sequences: A131832 A131833 A131834 * A131836 A131837 A131838

Keyword

nonn,base,easy

Author

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

Extensions

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

Status

approved