cp's OEIS Frontend

A233267 a(n) = A055881(A001110(n)); the largest m such that m! divides the n-th positive number which is both triangular and square.

%I A233267 #25 Feb 22 2019 02:01:39
%S A233267 1,3,1,4,1,3,1,4,1,3,1,7,1,3,1,4,1,3,1,4,1,3,1,7,1,3,1,4,1,3,1,4,1,3,
%T A233267 1,7,1,3,1,4,1,3,1,4,1,3,1,11,1,3,1,4,1,3,1,4,1,3,1,7,1,3,1,4,1,3,1,4,
%U A233267 1,3,1,7,1,3,1,4,1,3,1,4,1,3,1,7,1,3,1,4,1,3,1,4,1,3,1
%N A233267 a(n) = A055881(A001110(n)); the largest m such that m! divides the n-th positive number which is both triangular and square.
%C A233267 The sequence seems to have a nice symmetric fractal structure. The new distinct values (records) occur at positions k = 1, 2, 4, 12, 48, 288, 2016, 4032, ... those values being 1, 3, 4, 7, 11, 12, 13, 14, ...
%C A233267 Furthermore, each prefix from 1 to 2*k-1 (centered on a new record) seems to be palindromic. 2*k-1 runs as: 1, 3, 7, 23, 95, 575, 4031, 8063, ...
%C A233267 On the other hand, if we list ALL the positions p where prefix 1..p is palindromic, we obtain a sequence: 1, 3, 7, 11, 23, 35, 47, 95, 143, 191, 239, 287, 575, 863, 1151, 1439, 1727, 2015, 4031, ...
%C A233267 Its first differences is again familiar: 2, 4, 4, 12, 12, 12, 48, 48, 48, 48, 48, 288, 288, 288, 288, 288, 288, 2016, ... which appear to consist of 1, 2, 3, 5, 6, ... copies of the first mentioned sequence from its term 2 onward.
%C A233267 None of these sequences (except maybe the last) are in the OEIS as of Dec 06 2013.
%C A233267 Note: A233269(n) = A055881(A001109(n)) seems to have the same overall structure, but some of the records are missing/different.
%H A233267 Antti Karttunen, <a href="/A233267/b233267.txt">Table of n, a(n) for n = 1..8063</a>
%F A233267 a(n) = A055881(A001110(n)).
%o A233267 (Scheme)
%o A233267 (define (A233267 n) (A055881 (A001110 n)))
%Y A233267 Cf. A001110, A055881, A233269, A232096-A232098, A233285.
%K A233267 nonn
%O A233267 1,2
%A A233267 _Antti Karttunen_, Dec 06 2013