A384433 -id:A384433 - cp's OEIS frontend

A160851 Numbers which are a difference of two of their own anagrams.

459, 495, 1089, 1269, 1467, 1476, 1503, 1530, 1692, 1746, 2385, 2439, 2493, 2502, 2520, 2538, 2691, 2853, 3285, 3501, 3510, 4095, 4392, 4590, 4599, 4671, 4698, 4797, 4896, 4932, 4950, 4959, 4968, 4977, 4986, 4995, 5238, 5382, 5409, 6147, 6174, 6921, 8019, 8091

Offset: 1

Claudio Meller, May 28 2009

An anagram of a number k is a number formed by one of the k! permutations of its digits.

All terms are divisible by 9. - David A. Corneth, Jun 06 2025

			459 = 954 - 495;
495 = 954 - 459;
1089 = 9108 - 8019;
1269 = 2961 - 1692;
1467 = 7641 - 6174;
1476 = 6147 - 4671;
2538 = 5823 - 3285;
6174 = 7641 - 1467;
10989 = 91908 - 80919;
12969 = 29961 - 16992.

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Gonzalo Martínez)
David A. Corneth, PARI program

Cf. A055098, A384433.

PARI
```
\\ See Corneth link
```

from itertools import permutations
def ok(k):
    anagram = {int(''.join(p)) for p in permutations(str(k)) if p[0] != '0'}
    anagram.discard(k)
    return any(a != b and a - b == k for a in anagram for b in anagram)
print([k for k in range(10, 10000) if ok(k)]), #Gonzalo Martínez, May 28 2025

Definition edited by R. J. Mathar, May 30 2009

a(1), a(5)-a(15) inserted by Gonzalo Martínez May 28 2025

A384708 a(n) is the smallest integer k such that k is the sum of exactly n distinct permutations of k, all having the same number of digits as k.

Original entry on oeis.org

1, 954, 4617, 5112, 8136, 67104, 76011, 90216, 910107

Offset: 1

Gonzalo Martínez, Jun 07 2025

There is no such k exists for n >= 10, since the sum of 10 or more distinct permutations of any integer k, with the same number of digits of k, will always be greater than k itself.

			a(1) = 1, since 1 = 1.
a(2) = 954, since 954 = 459 + 495.
a(3) = 4617, since 4617 = 1467 + 1476 + 1674.
a(4) = 5112, since 5112 = 1125 + 1215 + 1251 + 1521.
a(5) = 8136, since 8136 = 1368 + 1386 + 1683 + 1836 + 1863.
a(6) = 67104, since 67104 = 10467 + 10476 + 10647 + 10674 + 10764 + 14076.
a(7) = 76011, since 76011 = 10167 + 10176 + 10617 + 10671 + 11067 + 11607 + 11706.
a(8) = 90216, since 90216 = 10269 + 10296 + 10629 + 10692 + 10962 + 12069 + 12609 + 12690.
a(9) = 910107, since 910107 = 100179 + 100197 + 100917 + 100971 + 101079 + 101097 + 101790 + 101907 + 101970. - _David A. Corneth_, Jun 12 2025

Subsequence of A384433.

Cf. A055098.

a(9) from David A. Corneth, Jun 12 2025

cp's OEIS Frontend

A160851 Numbers which are a difference of two of their own anagrams.

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