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

1,1

Comments

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

Links

Table of n, a(n) for n=1..31.

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 *)

Prog

(Java) import java.util.*; public class GenerateSequence {public static void main(String[] args) { Set<Integer> seq = new TreeSet<Integer>();
for (long i = 987654321l; i > 123456789; i--) {Set<Character> set = new HashSet<Character>(); 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); } }

Crossrefs

Sequence in context: A251474 A251468 A098765 * A062043 A331468 A124620

Adjacent sequences: A286842 A286843 A286844 * A286846 A286847 A286848

Keyword

nonn,base,fini,full

Author

Jonathan Schwartz, Aug 01 2017

Status

approved