A286846 Zeroless pandigital (9-digit) numbers where the first three digits minus the middle three digits equals the last three digits.

459173286, 459176283, 459183276, 459186273, 459273186, 459276183, 459283176, 459286173, 468173295, 468175293, 468193275, 468195273, 468273195, 468275193, 468293175, 468295173, 486127359, 486129357, 486157329, 486159327, 486327159, 486329157, 486357129

Offset: 1

Author

Jonathan Schwartz, Aug 01 2017

Keywords

• nonn
• base
• fini
• full

Examples

			459173286: 459 - 173 = 286.
		

Links

• Jonathan Schwartz, Table of n, a(n) for n = 1..336
• David A. Corneth, PARI program

Crossrefs

Cf. A050289, A286845, A289544, A289552.

A subsequence of A290725.

Programs

Java

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); } }

Mathematica

FromDigits/@Select[Permutations[Range[9]],FromDigits[Take[#,3]]-FromDigits[ Take[ #,{4,6}]]==FromDigits[Take[#,-3]]&] (* Harvey P. Dale, Aug 08 2020 *)

Python

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