cp's OEIS Frontend

A247305 The smaller of two consecutive triangular numbers which are permutations of each other.

%I A247305 #19 Oct 25 2014 23:29:03
%S A247305 404550,2653056,3643650,5633046,6413571,10122750,10656036,13762881,
%T A247305 19841850,26634051,32800950,47848653,56769840,71634465,89184690,
%U A247305 103672800,137108520,317053971,345069585,392714325,408508236,440762895,508948560,598735710,718830486,825215625
%N A247305 The smaller of two consecutive triangular numbers which are permutations of each other.
%C A247305 All the terms in sequence are congruent to 0 mod 9.
%C A247305 It appears that the digital root (repeated sum of digits) of the index +1 of a(n) in A000217 is 9 for each n>=1.o 0 mod 9. For example, 404550 = A000217(899), and 899+1 = 900 has digital root 9.
%H A247305 K. D. Bajpai, <a href="/A247305/b247305.txt">Table of n, a(n) for n = 1..13000</a>
%e A247305 a(1) = 404550 is in the sequence because {404550 and 405450} are a pair of consecutive triangular numbers having exactly the same digits.
%e A247305 a(2) = 2653056 is in the sequence because {2653056 and 2655360} are two consecutive triangular numbers having exactly the same digits.
%t A247305 A247305 = {}; a = {1}; b = {2}; Do[t1 = n*(n + 1)/2; t2 = (n - 1)*(n - 1 + 1)/2; b = Sort[IntegerDigits[t1]]; If[a == b, AppendTo[A247305, t2]]; a = b, {n, 2, 7*10^4}]; A247305
%o A247305 (PARI) lista(nn) = {for (n=1, nn, dt = vecsort(digits(t=n*(n+1)/2)); dnt = vecsort(digits((n+1)*(n+2)/2)); if (dt == dnt, print1(t, ", ")););} \\ _Michel Marcus_, Sep 13 2014
%Y A247305 Cf. A000217, A069567, A072274, A075093.
%K A247305 nonn,base
%O A247305 1,1
%A A247305 _K. D. Bajpai_, Sep 11 2014