cp's OEIS Frontend

A131835 Numbers starting with 1.

%I A131835 #44 Dec 07 2024 11:09:55
%S A131835 1,10,11,12,13,14,15,16,17,18,19,100,101,102,103,104,105,106,107,108,
%T A131835 109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,
%U A131835 126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142
%N A131835 Numbers starting with 1.
%C A131835 The lower and upper asymptotic densities of this sequence are 1/9 and 5/9, respectively. - _Amiram Eldar_, Feb 27 2021
%H A131835 Reinhard Zumkeller, <a href="/A131835/b131835.txt">Table of n, a(n) for n = 1..10000</a>
%H A131835 Bryan Brown, Michael Dairyko, Stephan Ramon Garcia, Bob Lutz and Michael Someck, <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.121.07.590">Four quotient set gems</a>, The American Mathematical Monthly, Vol. 121, No. 7 (2014), pp. 590-598; <a href="http://arxiv.org/abs/1312.1036">arXiv preprint</a>, arXiv:1312.1036 [math.NT], 2013.
%H A131835 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A131835 A000030(a(n)) = 1. - _Reinhard Zumkeller_, Jul 16 2014
%F A131835 a(A002275(n)+1) = 10^n for any n >= 0. - _Rémy Sigrist_, Jun 23 2017
%F A131835 a(n) = n + (8*10^floor(log_10(9*n-8))-8)/9. - _Alan Michael Gómez Calderón_, May 16 2023
%p A131835 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
%t A131835 Select[Range[150], IntegerDigits[#][[1]] == 1 &] (* _Amiram Eldar_, Feb 27 2021 *)
%o A131835 (Haskell)
%o A131835 a131835 n = a131835_list !! (n-1)
%o A131835 a131835_list = concat $
%o A131835                iterate (concatMap (\x -> map (+ 10 * x) [0..9])) [1]
%o A131835 -- _Reinhard Zumkeller_, Jul 16 2014
%o A131835 (PARI) a(n, {base=10}) = my (o=1); while (n>o, n-=o; o*=base); return (o+n-1) \\ _Rémy Sigrist_, Jun 23 2017
%o A131835 (PARI) a(n) = n--; s = #digits(9*n+1); n + 8 * (10^(s-1))/9 + 1/9 \\ _David A. Corneth_, Jun 23 2017
%o A131835 (PARI) nxt(n) = my(d = digits(n+1)); if(d[1]==1, n+1, 10^#d) \\ _David A. Corneth_, Jun 23 2017
%o A131835 (Python)
%o A131835 def A131835(n): return n+(10**(len(str(9*n-8))-1)<<3)//9 # _Chai Wah Wu_, Dec 07 2024
%Y A131835 Subsequence of A011531.
%Y A131835 Disjoint union of A045707 and A206286.
%Y A131835 Cf. A000030, A000027, A002275, A262390 (permutation).
%Y A131835 Cf. A217394, A217395, A217397, A217398, A217399, A217400, A217401, A217402.
%K A131835 nonn,base,easy
%O A131835 1,2
%A A131835 Andrew Good (yipes_stripes(AT)yahoo.com), Jul 20 2007
%E A131835 More terms from _R. J. Mathar_, Jul 24 2007