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

0,3

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

Links

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

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

Example

a(12) = 1 because 1 < 2.

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A054055.

Cf. A061601, A011540, A052382, A262188.

Sequence in context: A004176 A085124 A252648 * A115353 A031298 A004428

Adjacent sequences: A054051 A054052 A054053 * A054055 A054056 A054057

Keyword

base,easy,nonn

Author

Henry Bottomley, Apr 29 2000

Extensions

Edited by M. F. Hasler, Oct 11 2015

Status

approved