A063527 Numbers that are divisible by all of their 1 and 2 digit substrings.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 1111, 1155, 1248, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 27216, 31248, 111111, 116688, 121212, 142128, 212184, 222222, 242424, 313131, 321216, 333333, 363636, 368424, 444444

Offset: 1

Author

Erich Friedman, Aug 01 2001

Keywords

• base
• easy
• nonn

Comments

Subsequence of A034838. - Michel Marcus, Sep 19 2014

Examples

			1155 is divisible by 1, 1, 5, 5, 11, 15 and 55.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10442
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A034838 (integers divisible by all their digits).

Programs

Mathematica

d12Q[n_]:=Module[{idn=IntegerDigits[n],idn2},idn2=FromDigits/@Partition[ idn,2,1];FreeQ[idn,0]&&And@@Divisible[n,idn]&&And@@Divisible[n,idn2]]; Select[Range[400000],d12Q] (* Harvey P. Dale, Aug 11 2015 *)

PARI

is(n) = {my(d = digits(n), t = 0); s = Set(d); if(s[1] == 0, return(0)); for(i = 1, 2, for(j = 1, #d - i + 1, t++; fr = fromdigits(vector(i, k, d[j+k-1])); if(n % fr != 0, return(0)); ) ); 1 } \\ David A. Corneth, Sep 17 2019

Python

from itertools import product
A063527_list = []
for g in range(1,7):
    for n in product('123456789', repeat=g):
        s = ''.join(n)
        m = int(s)
        if not any([m % int(d) for d in s]):
            for i in range(len(s)-1):
                if m % int(s[i:i+2]):
                    break
            else:
                A063527_list.append(m) # Chai Wah Wu, Sep 18 2014

Extensions

More terms from David A. Corneth, Sep 17 2019