A286845 Every 3-digit number 'a' such that there exist two other 3-digit numbers, 'b' and 'c', such that a - b = c, and a,b,c collectively use every digit 1-9 exactly once.

459, 468, 486, 495, 549, 567, 576, 594, 639, 648, 657, 675, 693, 729, 738, 783, 792, 819, 837, 846, 864, 873, 891, 918, 927, 936, 945, 954, 963, 972, 981

Offset: 1

Author

Jonathan Schwartz, Aug 01 2017

Keywords

• nonn
• base
• fini
• full

Comments

For example, 459 - 173 = 286 and 459173286 is a zeroless pandigital number.

Programs

Java

import java.util.*; public class GenerateSequence {public static void main(String[] args) { Set seq = new TreeSet();
for (long i = 987654321l; i > 123456789; 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(Integer.valueOf(number.substring(0, 3)));} } } System.out.println(seq); } }

Mathematica

With[{s = Select[Range[#/9, #] &[10^3 - 1], DigitCount[#, 10, 0] == 0 &]}, Select[s, Function[n, AnyTrue[s, Function[k, And[n - k > 0, FreeQ[#, i_ /; i == 0], Length@ # == 9] &@ Union@ Apply[Join, IntegerDigits@ {n, k, n - k}]]]]]] (* Michael De Vlieger, Aug 01 2017 *)