cp's OEIS Frontend

A293700 First differences of A293698.

%I A293700 #30 Dec 16 2023 21:42:31
%S A293700 3,19,3,19,3,19,3,19,3,19,3,19,3,19,3,19,3,3,16,3,3,16,3,3,16,3,3,16,
%T A293700 3,3,19,3,19,3,19,3,19,3,19,3,19,3,19,3,19,3,19,3,19,3,19,3,19,3,3,16,
%U A293700 3,3,16,3,3,16,3,3,16,3,3,19,3,19,3,19,3,19,3,19,3
%N A293700 First differences of A293698.
%C A293700 Sequence seems to be composed of only three different integers: 3, 16 and 19.
%C A293700 Despite its apparent simplicity, it has interesting palindromic and periodic features and may be conjectured not to be represented in a closed form.
%C A293700 It has a resemblance to the sequences in DNA being composed of four nucleotide bases in varying orders. These sequences, too, contain palindromic substructures having an important role for the genome.
%C A293700 From _Robert Israel_, Nov 06 2017: (Start)
%C A293700 The only possible values are 3, 16 and 19.
%C A293700 k is in A293698 iff Pi/4 <= k - m*Pi < arctan(2) for some m. We may then verify the following:
%C A293700 If Pi/4 <= k - m*Pi < arctan(2) - 16 + 5*Pi, then k+16 is the next term of A293698.
%C A293700 If arctan(2) - 16 + 5*Pi <= k - m*Pi < 5*Pi/4 - 3, then k+19 is the next term of A293698.
%C A293700 If 5*Pi/4 - 3 <=  k - m*Pi < arctan(2), then k+3 is the next term of A293698. (End)
%H A293700 Robert Israel, <a href="/A293700/b293700.txt">Table of n, a(n) for n = 1..10000</a>
%p A293700 A293698:= select(i -> floor(tan(i))=1, [$1..1000]):
%p A293700 A293698[2..-1]-A293698[1..-2]; # _Robert Israel_, Nov 06 2017
%t A293700 rootsp = Flatten[Position[Table[Floor[Tan[i]], {i, 1, 10^6}], 1]];
%t A293700 difp = Differences[rootsp]
%t A293700 (*a(n)=difp[[n]]*)
%t A293700 Differences@ Select[ Range@750, Floor@ Tan@# == 1 &] (* _Robert G. Wilson v_, Nov 06 2017 *)
%o A293700 (PARI) lista(nn) = {last = 0; for (n=1, nn, if (floor(tan(n)) == 1, if (last, print1(n-last, ", ")); last = n;););} \\ _Michel Marcus_, Oct 24 2017
%Y A293700 Cf. A258200, A258007, A293701, A293704, A293698, A293751, A293699, A293702, A293705.
%K A293700 nonn
%O A293700 1,1
%A A293700 _V.J. Pohjola_, Oct 16 2017