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

1,2

Comments

Subsequence of A034838. - Michel Marcus, Sep 19 2014

Links

David A. Corneth, Table of n, a(n) for n = 1..10442

Index entries for 10-automatic sequences.

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A178158 A337184 A034838 * A209933 A182183 A308472

Adjacent sequences: A063524 A063525 A063526 * A063528 A063529 A063530

Keyword

base,easy,nonn

Author

Erich Friedman, Aug 01 2001

Extensions

More terms from David A. Corneth, Sep 17 2019

Status

approved