cp's OEIS Frontend

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.

%I A331468 #19 Feb 03 2020 00:04:50
%S A331468 459,495,954,1089,8019,9108,1089,8091,9180,1269,1692,2961,1467,6147,
%T A331468 7614,1467,6174,7641,1476,4671,6147,1503,3510,5013,1530,3501,5031,
%U A331468 1746,4671,6417,2385,2853,5238,2439,2493,4932,2502,2520,5022,2538,3285,5823,2691,6921,9612,2853,5382,8235,3285,5238,8523
%N 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.
%C A331468 The sequence is infinite as (10*A,10*B,10*C) is a legal triple if (A,B,C) is a legal triple.
%C A331468 From _Bernard Schott_, Jan 19 2020: (Start)
%C A331468 Theorem: Every term of this sequence is divisible by 9.
%C A331468 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)
%C A331468 The numbers of 3-digit to 8-digit triples are: 1, 25, 648, 17338, 495014, and 17565942. - _Hans Havermann_, Feb 02 2020
%H A331468 Gilles Esposito-Farèse, <a href="/A331468/b331468.txt">Table of n, a(n) for n = 1..50000</a>
%e A331468 The first triple is (459,495,954) and we have 459 + 495 = 954, anagrams of each other;
%e A331468 The second triple is (1089,8019,9108) and we have 1089 + 8019 = 9108, anagrams of each other;
%e A331468 The third triple is (1089,8091,9180) and we have 1089 + 8091 = 9180, anagrams of each other;
%e A331468 The fourth triple is (1269,1692,2961) and we have 1269 +1692 = 2961, anagrams of each other; etc.
%Y A331468 Cf. A160851, A203024, A121969, A055160, A055161, A055162.
%K A331468 base,nonn,tabf
%O A331468 1,1
%A A331468 _Eric Angelini_ and Gilles Esposito-Farèse, Jan 17 2020