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.
a254323 = a137564 . a254143
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
459173286: 459 - 173 = 286.
import java.util.*; public class GenerateSequence {public static void main(String[] args) { Set seq = new TreeSet(); for (long i = 123456789l; i < 987654321; i++) {Set set = new HashSet(); String number = Long.toString(i);if (!(number.contains("0"))) {for (int n = 0; n < 9; n++){set.add(number.charAt(n));} if (set.size() == 9) {if (Integer.valueOf(number.substring(0, 3)) - Integer.valueOf(number.substring(3, 6)) == Integer.valueOf(number.substring(6, 9))) { seq.add(i);} } } System.out.println(seq); } }
FromDigits/@Select[Permutations[Range[9]],FromDigits[Take[#,3]]-FromDigits[ Take[ #,{4,6}]]==FromDigits[Take[#,-3]]&] (* Harvey P. Dale, Aug 08 2020 *)
from itertools import permutations
def t2i(t): return int("".join(map(str, t)))
alst = [t2i(p) for p in permutations(range(1, 10)) if t2i(p[:3]) - t2i(p[3:6]) == t2i(p[6:])]
print(alst) # Michael S. Branicky, May 30 2022
filter:= proc(n) local L;
L:= convert(convert(n,base,10),set);
L = {$0..max(L)}
end proc:
select(filter, [$0..3000]); # Robert Israel, Jun 10 2018
Select[Range[0,10000],Union[IntegerDigits[#]]==Range[0,Max[IntegerDigits[#]]]&]
isok(n) = if (n==0, return (1)); my(d=Set(digits(n))); (vecmin(d) == 0) && (vecmax(d) == #d - 1); \\ Michel Marcus, Jul 05 2018
Sequence of sets of n-digit numbers that are weakly polydivisible and strictly pandigital is (with A = 10):
{0}
{1}
{12}
{123,321}
{}
{}
{123654,321654}
{}
{38165472}
{381654729}
{381654729A}
Select[Range[10000], PrimeQ[10^# - 987654321] &] (* Robert Price, Dec 05 2019 *)
for(n=1,10^4,if(ispseudoprime(10^n-987654321),print1(n,", ")))
a(2) = 11225079 because A002275(2)*11225079 = 11*11225079 = 123475869 that contains all digits from 1 to 9 and 11225079 is the least number with this property.
isok(n) = my(d=digits(n)); vecmin(d) && (#Set(digits(n)) == 9);
a(n) = {if (n==1, return(123456789)); my(k=1); while(! isok(k*(10^n - 1)/9), k++); k;} \\ Michel Marcus, Sep 26 2019
124659783: 124 + 659 = 783.
import java.util.*;public class Sequence{public static void main(String[] args) {
for (long i = 123456789l; i < 987654321l; i++)
{Set set = new HashSet();String number = Long.toString(i);
if (!(number.contains("0"))) {
for (int n = 0; n < 9; n++) {set.add(number.charAt(n));}
if (set.size() == 9){
if(Integer.valueOf(number.substring(0,3))+Integer.valueOf(number.substring(3,6))==Integer.valueOf(number.substring(6,9)))
{System.out.print(i + ", ");}}}}}}
FromDigits/@Select[Permutations[Range[9]],FromDigits[Take[#,3]]+FromDigits[ Take[ #,{4,6}]] == FromDigits[Take[#,-3]]&] (* Harvey P. Dale, Oct 18 2022 *)
from itertools import permutations
def t2i(t): return int("".join(map(str, t)))
alst = [t2i(p) for p in permutations(range(1, 10)) if t2i(p[:3]) + t2i(p[3:6]) == t2i(p[6:])]
print(alst) # Michael S. Branicky, May 30 2022
polyQ[q_]:=And@@Table[Divisible[FromDigits[Take[q,k]],k],{k,Length[q]}];
normseqs[n_]:=Join@@Permutations/@Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1];
Sort[FromDigits/@Join@@Table[Select[normseqs[n]-1,First[#]>0&&polyQ[#]&],{n,8}]]
Triangle is:
{1}
{1,2}
{1,2,3}
{3,2,1}
{1,2,3,6,5,4}
{3,2,1,6,5,4}
{3,8,1,6,5,4,7,2}
{3,8,1,6,5,4,7,2,9}
{3,8,1,6,5,4,7,2,9,10}
polyQ[q_]:=And@@Table[Divisible[FromDigits[Take[q,k]],k],{k,Length[q]}];
Flatten[Table[Select[Permutations[Range[n]],polyQ],{n,8}]]
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