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.

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

Author

Eric Angelini and Gilles Esposito-Farèse, Jan 17 2020

Keywords

• base
• nonn
• tabf

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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