A354113 - OEIS

%I #12 May 17 2022 17:49:47

%S 10,10,12,13,14,15,16,17,18,19,100,101,102,103,104,105,106,107,108,

%T 109,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,

%U 136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153

%N The smallest number that contains all the digits of n in order but does not equal n.

%C If n begins with 1, then a(n) is obtained by inserting a 0 after it; otherwise a(n) is obtained by placing a 1 before n.

%H Jianing Song, <a href="/A354113/b354113.txt">Table of n, a(n) for n = 0..10000</a>

%F If 10^k <= n < 2*10^k, a(n) = n + 9*10^k; if 2*10^k <= n < 10^(k+1), a(n) = n + 10^(k+1).

%e The smallest number not equal to 19 containing the digits 1 and 9 in that order is 109, so a(19) = 109.

%e The smallest number not equal to 22 containing two 2's is 122, so a(22) = 122.

%o (PARI) a(n) = if(n==0, 10, my(k=logint(n,10)); if(n<2*10^k, n+9*10^k, n+10^(k+1)))

%o (Python)

%o def a(n):

%o     if n == 0: return 10

%o     s = str(n)

%o     return int(s[0]+"0"+s[1:]) if s[0] == "1" else int("1"+s)

%o print([a(n) for n in range(54)]) # _Michael S. Branicky_, May 17 2022

%Y Cf. A354049, A354114.

%K nonn,base,easy

%O 0,1

%A _Jianing Song_, May 17 2022