A354049 The smallest number that includes all the digits of n but does not equal n.

10, 10, 12, 13, 14, 15, 16, 17, 18, 19, 100, 101, 21, 31, 41, 51, 61, 71, 81, 91, 102, 12, 122, 32, 42, 52, 62, 72, 82, 92, 103, 13, 23, 133, 43, 53, 63, 73, 83, 93, 104, 14, 24, 34, 144, 54, 64, 74, 84, 94, 105, 15, 25, 35, 45, 155, 65, 75, 85, 95, 106, 16, 26, 36, 46, 56, 166, 76, 86, 96, 107

Offset

0,1

Comments

The terms cannot start with a leading zero so any number including a zero must have at least one digit greater than zero as its first digit. See the examples below.

Links

Scott R. Shannon, Table of n, a(n) for n = 0..9999

Scott R. Shannon, Image of the first 100000 terms. The green line is y = n.

Example

a(9) = 19 as there is no smaller number that includes the digit 9 but does not equal 9.
a(10) = 100 as there is no smaller number that includes the digits 1 and 0 but does not equal 10. Note that '01' = 1 is not allowed.
a(20) = 102 as there is no smaller number that includes the digits 2 and 0 but does not equal 20. Note that '02' = 2 is not allowed.
a(22) = 122 as there is no smaller number that includes two 2 digits but does not equal 22.
a(200) = 1002 as there is no smaller number that includes two 0 digits and the digit 2 but does not equal 200.

Prog

(PARI) vd(n) = my(d=if (n, digits(n), [0])); vector(10, k, #select(x->(x==k-1), d));
isok(k, n, d) = if (k!=n, my(dd=vd(k)); for (i=1, #d, if (dd[i] < d[i], return(0))); return(1));
a(n) = my(k=0, d=vd(n)); while(!isok(k, n, d), k++); k; \\ Michel Marcus, May 17 2022
(Python)
def ok(k, n):
    if k == n: return False
    sk, sn = str(k), str(n)
    return all(sk.count(d) >= sn.count(d) for d in set(sn))
def a(n):
    k = 0
    while not ok(k, n): k += 1
    return k
print([a(n) for n in range(71)]) # Michael S. Branicky, May 23 2022

Crossrefs

Cf. A004185, A004185, A337227.

Sequence in context: A111381 A369604 A063660 * A354113 A354114 A175220

Adjacent sequences: A354046 A354047 A354048 * A354050 A354051 A354052

Keyword

nonn,base,look

Author

Scott R. Shannon and Zach J. Shannon, May 16 2022

Status

approved