OFFSET
1,2
COMMENTS
This is a subset of some of the related sequences listed below. Stephen Lynch and Andrew Bell are Brisbane surgeons who contributed to the identification of this sequence.
There are 548 Lynch-Bell numbers. A117911 gives the number of n-digit ones. The digit 5 cannot appear in Lynch-Bell numbers containing an even digit; 5 must be the units digit when it appears. The 7-digit Lynch-Bell numbers are 105 permutations of 1289736 (the smallest such). - Rick L. Shepherd, Apr 01 2006
Can be seen/read as a table with row lengths A117911 (rows r > 7 have zero length). - M. F. Hasler, Jan 31 2016
LINKS
Rick L. Shepherd, List of all terms
EXAMPLE
384/3 = 128, 384/8 = 48, 384/4 = 96. Thus 384 is Lynch-Bell as it is a multiple of each of its three distinct digits.
MAPLE
with(combinat):
f:= l-> parse(cat(l[])):
T:= n-> sort(map(f, select(l-> andmap(x-> irem(f(l), x)=0, l),
map(p-> permute(p)[], choose([$1..9], n)))))[]:
seq(T(n), n=1..7); # Alois P. Heinz, Jul 31 2022
MATHEMATICA
Reap[For[n = 1, n < 10^7, n++, id = IntegerDigits[n]; If[FreeQ[id, 0] && Length[id] == Length[Union[id]] && And @@ (Divisible[n, #]& /@ id), Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Nov 26 2013 *)
bnQ[n_]:=Max[DigitCount[n]]==1&&FreeQ[IntegerDigits[n], 0]&&Union[Divisible[n, IntegerDigits[ n]]]=={True}; Select[Range[2000], lbnQ] (* Harvey P. Dale, Jun 02 2023 *)
Cases[Union @@ ((FromDigits@#&/@Flatten[Permutations@# & /@ Subsets[Range@9, {#}], 1])&/@ Range@9), _?(DeleteDuplicates[Divisible[#, IntegerDigits@#]] == {True} &)] (* Hans Rudolf Widmer, Aug 27 2024 *)
PROG
(PARI) A115569_row(n)={if(n, my(u=vectorv(n, i, 10^i)\10, S=List(), M); forvec(v=vector(n, i, [1, 9]), (M=lcm(v))%10==0||normlp(v, 1)%3^valuation(M, 3)||for(k=1, n!, vecextract(v, numtoperm(n, k))*u%M ||listput(S, vecextract(v, numtoperm(n, k))*u)), 2); Set(S), concat(apply(A115569_row, [1..7])))} \\ Return terms of length n if given, else the vector of all terms. The checks M%10 and |v| % 3^v(...) are not needed but reduce CPU time by 97%. - M. F. Hasler, Jan 31 2016
(PARI) A115569(n)=n>9&&for(r=2, 7, (n-=#t=A115569_row(r))>9||return(t[n-9+#t])); n \\ M. F. Hasler, Jan 31 2016
(Python)
def ok(n):
s = str(n)
if "0" in s or len(set(s)) < len(s): return False
return all(n%int(d) == 0 for d in s)
afull = [k for k in range(9867313) if ok(k)]
print(afull[:55]) # Michael S. Branicky, Jul 31 2022
CROSSREFS
KEYWORD
base,easy,nonn,fini,full
AUTHOR
Mike Smith (mtm_king(AT)yahoo.com), Mar 10 2006; also submitted by Andy Edwards (AndynGen(AT)aol.com), Mar 20 2006
EXTENSIONS
The full list of terms was sent in by Rick L. Shepherd (see link) and also by Sébastien Dumortier, Apr 04 2006
STATUS
approved