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

1,1

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

Links

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

David A. Corneth, PARI program

Example

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.

Prog

(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
(PARI) \\ See Corneth link

Crossrefs

Cf. A055098, A384433.

Sequence in context: A286845 A062043 A331468 * A124620 A224456 A121970

Adjacent sequences: A160848 A160849 A160850 * A160852 A160853 A160854

Keyword

nonn,base

Author

Claudio Meller, May 28 2009

Extensions

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

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

Status

approved