This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
With[{t=Sort[FromDigits[Join[{1},#]]&/@Permutations[{2,3,4,5,6,7,8,9,0}]]}, Flatten[ Table[Select[t,Divisible[#,n]&,1],{n,20}]]] (* Harvey P. Dale, Aug 26 2014 *)
a(5)=19: 5^19 = 19073486328125.
a:= proc(n) local k;
if n = 10^ilog10(n) then return 0 fi;
for k from 1 do
if nops(convert(convert(n^k,base,10),set))=10 then return k fi
od
end proc:
seq(a(n),n=1..100); # Robert Israel, Aug 20 2014
Table[If[IntegerQ@ Log10[n], 0, SelectFirst[Range[#, # + 100] &@ Ceiling[9 Log[n, 10]], NoneTrue[DigitCount[n^#], # == 0 &] &]], {n, 71}] (* Michael De Vlieger, Sep 06 2017 *)
a(n) = if (n == 10^valuation(n, 10), return (0)); k=1; while(#vecsort(digits(n^k),,8)!=10, k++); k; \\ Michel Marcus, Aug 20 2014
def a(n):
s = str(n)
if n == 1 or (s.count('0')==len(s)-1 and s.startswith('1')):
return 0
k = 1
count = 0
while count != 10:
count = 0
for i in range(10):
if str(n**k).count(str(i)) == 0:
count += 1
break
if count:
k += 1
else:
return k
n = 1
while n < 100:
print(a(n), end=', ')
n += 1
# Derek Orr, Aug 20 2014
nextp:= proc(L) local m, i,j, r, rj;
for m from 2 while L[m-1] <= L[m] do od:
r:= 10:
for j from 1 to m-1 do
if L[j] > L[m] and L[j] < r then
r:= L[j]; rj:= j;
fi
od;
[ op(sort([seq(L[i],i={$1..m} minus {rj})],`>`)), r,seq(L[i],i=m+1..nops(L))]
end proc:
A[1]:= 10012233445566778899:
L:= convert(A[1],base,10):
for n from 2 to 100 do
L:= nextp(L);
A[n]:= add(L[i]*10^(i-1),i=1..nops(L));
od:
seq(A[i],i=1..100); # Robert Israel, Feb 25 2019
is_A215876(N)={my(c=vector(10)); for(k=1,#N=Vecsmall(Str(N)), c[N[k]-47]++); vecmin(c)>1}
import Data.List ((\\)) a230959 n = (if null cds then 0 else read cds) :: Integer where cds = "9876543210" \\ show n
pd[n_]:=Module[{idn=Sort[IntegerDigits[n]]},If[idn==Range[0,9],0,FromDigits[ Reverse[ Complement[ Range[ 0,9],idn]]]]]; Table[pd[n],{n,0,30}] (* Harvey P. Dale, Nov 16 2023 *)
def A230959(n): return int(''.join(sorted(set('9876543210')-set(str(n)),reverse=True)) or 0) # Chai Wah Wu, Nov 23 2022
a(11) = 41 as 11^41 = 4978518112499354698647829163838661251242411 is the conjectural highest power of 11 not containing all ten digits. a(110) = 38 as 110^38 does not contain the digit 2, while, conjecturally, all higher powers of 110 contain all ten digits. - _Christopher J. Smyth_, Aug 20 2014
Select[Range[10^7, 10^7 + 1000000], Length[Union[IntegerDigits[#]]] == 8 &] (* T. D. Noe, Dec 05 2012 *)
a(2) is 2 because it is the smallest number not yet used where the digits of a(1)/a(2) = .5, i.e., 5, is neither 1 nor 2. a(3) is 3 because it is the smallest number not yet used where the digits of a(2)/a(3) = .666.., i.e., 6, is neither 2 nor 3. a(4) is 4 because it is the smallest number not yet used where the digits of a(3)/a(4) = .75, i.e., 5 and 7, are neither 3 nor 4. a(72) is 63 because it is the smallest number not yet used where the digits of a(71)/a(72) = 90/63 = 1.42857142857.., i.e., 1, 2, 4, 5, 7, and 8, are not any of 0, 3, 6, or 9. a(376) is 15000 because it is the smallest number not yet used where the digits of a(375)/a(376) = 1025/15000 = .068333.., i.e., 3, 6, and 8 (the zero is leading) are not any of 0, 1, 2, or 5.
t = 1; s = {1}; Do[c = 1; d = IntegerDigits[t]; While[Intersection[Flatten[RealDigits[t/c][[1]]], Join[IntegerDigits[c], d]] != {} || MemberQ[s, c], c++]; t = c; AppendTo[s, t], {400}]; s
a(n)=if(n<9,return(n)); my(d=Set(digits(n))); sum(k=1,n-1, #setintersect(d, Set(digits(k)))==0)+(d[1]>0) \\ Charles R Greathouse IV, Dec 02 2013
a(1) is 15628 = 4 * 3907, using all 10 digits. a(8) is 20748 = 13 * 1596 (note duplicate 1, which is ok in this sequence). a(3) is 16038 = 27 * 594, and also 16038 = 54 * 297; two different solutions for a(3).
import Data.List (nub, sort)
a253172 n = a253172_list !! (n-1)
a253172_list = filter f [2..] where
f x = g divs $ reverse divs where
g (d:ds) (q:qs) = d <= q &&
(sort (nub $ xs ++ show d ++ show q) == decs || g ds qs)
xs = show x
divs = a027750_row x
decs = "0123456789"
-- Reinhard Zumkeller, Dec 29 2014
isokpq(n) = {fordiv(n, d, digs = digits(n); if ( d <= sqrtint(n), digs = concat(digs, digits(d)); digs = concat(digs, digits(n/d)); if (#Set(digs) == 10, return(1));););}
lista(nn) = {for(n=2, nn, if (isokpq(n), print1(n, ", ")););} \\ Michel Marcus, Dec 29 2014
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