A289552 Zeroless pandigital numbers (each digit 1-9 used exactly once) where the first 3 digits plus the next 3 digits equals the last 3 digits.

124659783, 125739864, 127359486, 127368495, 128367495, 128439567, 129357486, 129438567, 129654783, 129735864, 134658792, 135729864, 138429567, 138654792, 139428567, 139725864, 142596738, 142695837, 143586729, 145692837, 146583729, 146592738, 152487639, 152784936

Offset: 1

Author

Jonathan Schwartz, Aug 02 2017

Keywords

• nonn
• base
• fini
• full

Examples

			124659783: 124 + 659 = 783.
		

Links

• Jonathan Schwartz, Table of n, a(n) for n = 1..336
• David A. Corneth, PARI program
• Eric Weisstein, World of Mathematics, Pandigital Number.

Crossrefs

Cf. A050289, A286846, A289544.

Programs

Java

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 + ", ");}}}}}}

Mathematica

FromDigits/@Select[Permutations[Range[9]],FromDigits[Take[#,3]]+FromDigits[ Take[ #,{4,6}]] == FromDigits[Take[#,-3]]&] (* Harvey P. Dale, Oct 18 2022 *)

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