A131835 - OEIS (original) (raw)

A131835

Numbers starting with 1.

26

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

COMMENTS

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

LINKS

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.

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]

(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

AUTHOR

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