A354114 The smallest number that contains all the digits of n as a substring but does not equal n.

10, 10, 12, 13, 14, 15, 16, 17, 18, 19, 100, 110, 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, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153

Offset

0,1

Comments

Suppose that n > 0 is a k-digit number. If 10^(k-1) <= a(n) <= (10^k-1)/9, then a(n) is obtained by placing a 0 after n; otherwise a(n) is obtained by placing a 1 before n.

Links

Jianing Song, Table of n, a(n) for n = 0..10000

Formula

If 10^k <= n <= (10^(k+1)-1)/9, a(n) = 10*n; if (10^(k+1)-1)/9 <= n < 10^(k+1), a(n) = n + 10^(k+1).

Example

The smallest number not equal to 111 containing the substring "111" in its decimal expansion is 1110, so a(111) = 1110.
The smallest number not equal to 112 containing the substring "112" in its decimal expansion is 1112, so a(112) = 1112.

Prog

(PARI) a(n) = if(n==0, 10, my(k=logint(n, 10)); if(n<=10^(k+1)\9, 10*n, n+10^(k+1)))
(Python)
def a(n):
    if n == 0: return 10
    s = str(n)
    return n*10 if s <= "1"*len(s) else int("1"+s)
print([a(n) for n in range(54)]) # Michael S. Branicky, May 17 2022

Crossrefs

Cf. A354049, A354113.

Sequence in context: A063660 A354049 A354113 * A175220 A272479 A167427

Adjacent sequences: A354111 A354112 A354113 * A354115 A354116 A354117

Keyword

nonn,base,easy

Author

Jianing Song, May 17 2022

Status

approved