A054054 Smallest digit of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 0, 1, 2, 3, 4, 4, 4, 4, 4, 4, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 0, 1, 2, 3, 4, 5, 6, 6, 6, 6, 0, 1, 2, 3, 4, 5, 6, 7, 7, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0

Offset: 0

Author

Henry Bottomley, Apr 29 2000

Keywords

• base
• easy
• nonn

Comments

a(n) = 0 for almost all n. - Charles R Greathouse IV, Oct 02 2013

More precisely, a(n) = 0 asymptotically almost surely, i.e., except for a set of density 0: As the number of digits of n grows, the probability of having no zero digit goes to zero as 0.9^(length of n), although there are infinitely many counterexamples. - M. F. Hasler, Oct 11 2015

Examples

			a(12) = 1 because 1 < 2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A054055.

Cf. A061601, A011540, A052382, A262188.

Programs

Haskell

a054054 = f 9 where
   f m x | x <= 9 = min m x
         | otherwise = f (min m d) x' where (x',d) = divMod x 10
-- Reinhard Zumkeller, Jun 20 2012, Apr 25 2012

Maple

seq(min(convert(n,base,10)),n=0..100); # Robert Israel, Jul 07 2016

Mathematica

A054054[n_]:=Min[IntegerDigits[n]]

PARI

A054054(n)=if(n,vecmin(digits(n)))  \\ or: Set(digits(n))[1]. - M. F. Hasler, Jan 23 2013

Formula

a(A011540(n)) = 0; a(A052382(n)) > 0. - Reinhard Zumkeller, Apr 25 2012

a(n) = A262188(n,0). - Reinhard Zumkeller, Sep 14 2015

a(n) = 0 iff A007954(n) = 0. - M. F. Hasler, Oct 11 2015

a(n) = 9 - A054055(A061601(n)). - Robert Israel, Jul 07 2016

Extensions

Edited by M. F. Hasler, Oct 11 2015