A286846 -id:A286846 - cp's OEIS frontend

A289544 Pandigital numbers (each digit 0-9 used exactly once) where the first 3 digits plus the next 3 digits equals the last 4 digits.

2467891035, 2497861035, 2647891053, 2697841053, 2847691053, 2867491035, 2897461035, 2897641053, 3247651089, 3257641089, 3427561098, 3467521098, 3478591206, 3498571206, 3527461098, 3567421098, 3578491206, 3598471206, 3647251089, 3657241089, 4236751098, 4256731098

Offset: 1

Jonathan Schwartz, Aug 02 2017

Leading zeros in the last four digits are not included, else 1246590783, with 124 + 659 = 783 would be the first term.

			2467891035 is in the sequence as 246|789|1035: 246 + 789 = 1035 and each digit (0-9) is used exactly once.

Jonathan Schwartz, Table of n, a(n) for n = 1..96
David A. Corneth, PARI program

Cf. A050278, A289552, A286846.

FromDigits /@ Select[Permutations[Range[0, 9]], And[#1 + #2 == #3, #3 >= 1000] & @@ Map[FromDigits, {Take[#, 3], #[[4 ;; 6]], Take[#, -4]}] &] (* Michael De Vlieger, Aug 02 2018 *)

from itertools import permutations
def t2i(t): return int("".join(map(str, t)))
alst = [t2i(p) for p in permutations(range(10)) if p[6] != 0 and t2i(p[:3]) + t2i(p[3:6]) == t2i(p[6:])]
print(alst) # Michael S. Branicky, May 30 2022

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.

Original entry on oeis.org

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

Jonathan Schwartz, Aug 02 2017

			124659783: 124 + 659 = 783.

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

Cf. A050289, A286846, A289544.

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

A290725 Numbers with 3k digits for some k such that the first k digits minus the middle k digits equals the last k digits.

Original entry on oeis.org

101, 110, 202, 211, 220, 303, 312, 321, 330, 404, 413, 422, 431, 440, 505, 514, 523, 532, 541, 550, 606, 615, 624, 633, 642, 651, 660, 707, 716, 725, 734, 743, 752, 761, 770, 808, 817, 826, 835, 844, 853, 862, 871, 880, 909, 918, 927, 936, 945, 954, 963, 972, 981, 990, 100010, 100109, 100208, 100307

Offset: 1

N. J. A. Sloane, Aug 09 2017

			987654333 is a member because 987-654=333.

Robert Israel, Table of n, a(n) for n = 1..10000

A286846 is a subsequence.

N:= 100: # to get the first N terms
count:= 0:
Res:= NULL:
for d from 1 while count < N do
  for x1 from 10^(d-1) to 10^d-1 while count < N do
    for x2 from 0 to x1 while count < N do
      x3:= x1 - x2;
      count:= count+1;
      Res:= Res, x1*10^(2*d)+x2*10^d+x3;
od od od:
Res; # Robert Israel, Aug 09 2017

kd3Q[n_]:=Module[{c=FromDigits/@Partition[IntegerDigits[n], IntegerLength[ n]/3]},c[[1]]-c[[2]]==c[[3]]]; Table[Select[Range[10^(3n-1),10^(3n)-1], kd3Q],{n,2}]//Flatten (* Harvey P. Dale, Feb 25 2020 *)

More terms from Robert Israel, Aug 09 2017

cp's OEIS Frontend

A289544 Pandigital numbers (each digit 0-9 used exactly once) where the first 3 digits plus the next 3 digits equals the last 4 digits.

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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.

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Author

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Programs

Java

Mathematica

Python

A290725 Numbers with 3k digits for some k such that the first k digits minus the middle k digits equals the last k digits.

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Keywords

Examples

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Maple

Mathematica

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