# [seqfan] a(n) is divisible by the a(n)th digit of S

Eric Angelini Eric.Angelini at kntv.be
Wed Mar 21 15:34:32 CET 2012

```Hello again, SeqFans (last msg 4 2 D),

a(n) is the smallest integer not yet present in S such that
a(n) is divisible by the a(n)th digit of S (if you have to
divide by zero, divide by 10 instead):

S = 1,2,3,4,5,6,7,8,9,10,20,12,30,11,14,15,40,13,16,17,24,
18,25,28,50,19,21,22,36,23,35,26,32,27,48,34,45,38,56,55,
60,29,54,42,31,44,46,51,66,50,57,63,...
Done by hand in a couple of minutes -- could someone please
check and submit, if of interest?
Best,
É.                                                a(n)th digit of S:
(example -- NYiS means "not yet in S")                            |
the smallest NYiS integer divisible by the 1st digit of S is 1    1
the smallest NYiS integer divisible by the 2nd digit of S is 2    2
the smallest NYiS integer divisible by the 3rd digit of S is 3    3
the smallest NYiS integer divisible by the 4th digit of S is 4    4
the smallest NYiS integer divisible by the 5th digit of S is 5    5
the smallest NYiS integer divisible by the 6th digit of S is 6    6
the smallest NYiS integer divisible by the 7th digit of S is 7    7
the smallest NYiS integer divisible by the 8th digit of S is 8    8
the smallest NYiS integer divisible by the 9th digit of S is 9    9
the smallest NYiS integer divisible by the 10th digit of S is 10  1
the smallest NYiS integer divisible by the 11th digit of S is 20  0
(as the 11th digit of S is zero, a(n) must be divisible by 10)
the smallest NYiS integer divisible by the 12th digit of S is 12  2
the smallest NYiS integer divisible by the 13th digit of S is 30  0
the smallest NYiS integer divisible by the 14th digit of S is 11  1
the smallest NYiS integer divisible by the 15th digit of S is 14  2
the smallest NYiS integer divisible by the 16th digit of S is 15  3
the smallest NYiS integer divisible by the 17th digit of S is 40  0
the smallest NYiS integer divisible by the 18th digit of S is 13  1
the smallest NYiS integer divisible by the 19th digit of S is 16  1
the smallest NYiS integer divisible by the 20th digit of S is 17  1
the smallest NYiS integer divisible by the 21st digit of S is 24  4
...)
S is a permutation of the Natural numbers.
Best,
É.

```