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%I #15 Apr 20 2024 09:58:07
%S 1,3,6,55,66,666,1128,1326,2346,31626,133386,193131,212226,236328,
%T 283128,416328,881128,1211346,1222266,1466328,1777555,2263128,
%U 11293128,14191128,16111326,16316328,22121226,22261128,26263128,31621128,32292666,33321366,33533955,39139128
%N Triangular numbers (A000217) in A353729.
%C Intersection of A000217 and A353729.
%C The sequence is infinite because the numbers T(1327) = 881128, T(13327) = 88811128, T(133327) = 8888111128, ..... are terms.
%C Also, the numbers T(651) = 21226, T(6651) = 22121226, T(66651) = 2221211226, T(666651) = 222212111226.... or T(672) = 226128, T(6672) = 22261128, T(66672) = 2222611128, ... are terms.
%e 2346 = A000217(68) and 346 = 2*173, 246 = 3*82, 234 = 6*39, so 2346 is a term.
%o (Magma) ints:=func<n| n eq 0 select[0] else Intseq(n)>;f:=func<n,i|Seqint([ints(n)[j]:j in [1..#ints(n)]|j ne (#ints(n)-i+1)])>;[p:p in [s*(s+1) div 2:s in [1..10000]]|not 0 in ints(p) and forall{i:i in [1..#ints(p)]|IsIntegral( f(p,i)/ ints(p)[(#Intseq(p)-i+1)] )}];
%Y Cf. A000217, A353729, A367451.
%K nonn,base
%O 1,2
%A _Marius A. Burtea_, Feb 27 2024
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