A160851 -id:A160851 - cp's OEIS frontend

A384433 Integers k that are equal to the sum of at least two distinct of their anagrams, which must have the same number of digits as k.

954, 2961, 4617, 4851, 4932, 5013, 5022, 5031, 5103, 5112, 5184, 5238, 5823, 5913, 6012, 6021, 6102, 6129, 6147, 6171, 6180, 6192, 6210, 6219, 6291, 6312, 6321, 6417, 6519, 6915, 6921, 7125, 7128, 7149, 7152, 7182, 7194, 7218, 7251, 7281, 7341, 7416, 7431

Offset: 1

Gonzalo Martínez, May 28 2025

This sequence consists of integers k that are equal to the sum of at least two of their own digit permutations. All anagrams must have the same number of digits as k, so permutations with leading zeros are not allowed.
Unlike Osiris numbers (A319274), which are formed by summing permutations of digit subsamples, these numbers require the use of all digits in each term of the sum.
All terms are divisible by 3. Proof: if a term t is in the sequence then it is a sum of at least 2 anagrams and at most 9 anagrams. The remainder of any q anagrams of t is (q*t) mod 9 which is never equivalent t mod 9 since t mod 3 is nonzero. - David A. Corneth, Jun 05 2025

			4617 is in this list, since 4617 = 1467 + 1476 + 1674, where 1467, 1476 and 1674 are anagrams of 4617.
921 is not in the sequence even though 921 = 192 + 219 + 219 + 291. - _David A. Corneth_, Jun 05 2025

David A. Corneth, Table of n, a(n) for n = 1..10956 (first 500 terms from Gonzalo Martínez)

Cf. A055098, A319274, A160851.

from itertools import permutations
from functools import lru_cache
@lru_cache(maxsize=None)
def anagrams(k):
    s = str(k)
    return sorted({int(''.join(p)) for p in permutations(s) if p[0] != '0' and int(''.join(p)) != k})
def ok(k):
    def back(i, acc):
        if acc == k: return True
        if acc > k or i == len(a): return False
        return back(i + 1, acc + a[i]) or back(i + 1, acc)
    a = anagrams(k)
    return back(0, 0)
print([k for k in range(10, 10000) if ok(k)])

A331468 Lexicographically earliest sequence of distinct triples (A,B,C) such that A + B = C with A, B, C anagrams of each other and A < B.

Original entry on oeis.org

459, 495, 954, 1089, 8019, 9108, 1089, 8091, 9180, 1269, 1692, 2961, 1467, 6147, 7614, 1467, 6174, 7641, 1476, 4671, 6147, 1503, 3510, 5013, 1530, 3501, 5031, 1746, 4671, 6417, 2385, 2853, 5238, 2439, 2493, 4932, 2502, 2520, 5022, 2538, 3285, 5823, 2691, 6921, 9612, 2853, 5382, 8235, 3285, 5238, 8523

Offset: 1

Eric Angelini and Gilles Esposito-Farèse, Jan 17 2020

The sequence is infinite as (10*A,10*B,10*C) is a legal triple if (A,B,C) is a legal triple.
From Bernard Schott, Jan 19 2020: (Start)
Theorem: Every term of this sequence is divisible by 9.
Proof: If m = digsum(A) = digsum(B) = digsum(C) where digsum = A007953, then A + B = C implies digsum(A) + digsum(B) == digsum(C) (mod 9), so 2*m == m (mod 9) and m == 0 (mod 9). (End)
The numbers of 3-digit to 8-digit triples are: 1, 25, 648, 17338, 495014, and 17565942. - Hans Havermann, Feb 02 2020

			The first triple is (459,495,954) and we have 459 + 495 = 954, anagrams of each other;
The second triple is (1089,8019,9108) and we have 1089 + 8019 = 9108, anagrams of each other;
The third triple is (1089,8091,9180) and we have 1089 + 8091 = 9180, anagrams of each other;
The fourth triple is (1269,1692,2961) and we have 1269 +1692 = 2961, anagrams of each other; etc.

Gilles Esposito-Farèse, Table of n, a(n) for n = 1..50000

Cf. A160851, A203024, A121969, A055160, A055161, A055162.

cp's OEIS Frontend

A384433 Integers k that are equal to the sum of at least two distinct of their anagrams, which must have the same number of digits as k.

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