A373696 a(n) is the least m >= 0 with the same number of digits as n such that for some permutation p of 0..9, applying p to the digits of n yields the digits of m.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 10

Offset: 0

Author

Rémy Sigrist, Aug 04 2024

Keywords

• nonn
• base

Comments

Leading zeros are ignored.

For n > 0, a(n) is the least m > 0 such that A358497(n) = A358497(m).

All positive terms belong to A266946.

Examples

			For n = 65507668: the different digits appearing in 65507668 are 6, 5, 0, 7 and 8; so we replace 6's by 1's, 5's by 0's, 0's by 2's, 7's by 3's and 8's by 4's, and a(65507668) = 10023114.
		

Crossrefs

Cf. A137564, A266946, A358497, A373712 (ternary analog).

Programs

PARI

a(n, base = 10) = { my (d = digits(n, base), m = vector(base, i, -1), u = 1); for (i = 1, #d, if (m[1+d[i]] < 0, m[1+d[i]] = u; u = if (u==1, 0, u==0, 2, u+1);); d[i] = m[1+d[i]];); fromdigits(d, base); }

Formula

a(n) <= n with equality iff n = 0 or n belongs to A266946.

a(a(n)) = a(n).