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

%I A063527 #21 May 22 2025 10:21:34
%S A063527 1,2,3,4,5,6,7,8,9,11,12,15,22,24,33,36,44,48,55,66,77,88,99,1111,
%T A063527 1155,1248,2222,3333,4444,5555,6666,7777,8888,9999,27216,31248,111111,
%U A063527 116688,121212,142128,212184,222222,242424,313131,321216,333333,363636,368424,444444
%N A063527 Numbers that are divisible by all of their 1 and 2 digit substrings.
%C A063527 Subsequence of A034838. - _Michel Marcus_, Sep 19 2014
%H A063527 David A. Corneth, <a href="/A063527/b063527.txt">Table of n, a(n) for n = 1..10442</a>
%H A063527 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%e A063527 1155 is divisible by 1, 1, 5, 5, 11, 15 and 55.
%t A063527 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 *)
%o A063527 (Python)
%o A063527 from itertools import product
%o A063527 A063527_list = []
%o A063527 for g in range(1,7):
%o A063527     for n in product('123456789', repeat=g):
%o A063527         s = ''.join(n)
%o A063527         m = int(s)
%o A063527         if not any([m % int(d) for d in s]):
%o A063527             for i in range(len(s)-1):
%o A063527                 if m % int(s[i:i+2]):
%o A063527                     break
%o A063527             else:
%o A063527                 A063527_list.append(m) # _Chai Wah Wu_, Sep 18 2014
%o A063527 (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
%Y A063527 Cf. A034838 (integers divisible by all their digits).
%K A063527 base,easy,nonn
%O A063527 1,2
%A A063527 _Erich Friedman_, Aug 01 2001
%E A063527 More terms from _David A. Corneth_, Sep 17 2019