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

Author

Claudio Meller, May 28 2009

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A055098, A384433.

Programs

PARI

\\ See Corneth link

Python

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

Extensions

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

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