A121042 Smallest divisor of n that is also contained in the decimal representation of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 23, 2, 5, 2, 27, 2, 29, 3, 1, 2, 3, 34, 5, 3, 37, 38, 3, 4, 1, 2, 43, 4, 5, 46, 47, 4, 49, 5, 1, 2, 53, 54, 5, 56, 57, 58, 59, 6, 1, 2, 3, 4, 5, 6, 67, 68, 69, 7, 1, 2, 73, 74, 5, 76, 7, 78, 79, 8, 1, 2, 83, 4, 5, 86, 87, 8, 89, 9, 1

Offset: 1

Author

Reinhard Zumkeller, Jul 21 2006

Keywords

• nonn
• base

Comments

1 <= a(n) <= n;

a(A011531(n)) = 1; a(n) = n iff A121041(n) = 1.

a(n) = 1 for almost all n (measure 1). - Charles R Greathouse IV, Mar 31 2016

Examples

			a(48) = Min{4, 8, 48} = 4;
a(49) = Min{49} = 49;
a(120) = Min{1, 2, 12, 20, 120} = 1;
a(121) = Min{1} = 1.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A011531, A027750, A121041, A383749 (fixed points).

Programs

Mathematica

A121042[n_] := SelectFirst[Divisors[n], StringContainsQ[IntegerString[n], IntegerString[#]] &];
Array[A121042, 100] (* Paolo Xausa, May 12 2025 *)

PARI

substr(a,b)=a=digits(a);b=digits(b); for(i=0,#a-#b, for(j=1,#b, if(a[i+j]!=b[j], next(2))); return(1)); 0
a(n)=fordiv(n,d, if(substr(n,d), return(d))) \\ Charles R Greathouse IV, Mar 31 2016