A293700 First differences of A293698.

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, 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, 3, 3, 16, 3, 3, 16, 3, 3, 16, 3, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3

Offset

1,1

Comments

Sequence seems to be composed of only three different integers: 3, 16 and 19.

Despite its apparent simplicity, it has interesting palindromic and periodic features and may be conjectured not to be represented in a closed form.

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.

From Robert Israel, Nov 06 2017: (Start)

The only possible values are 3, 16 and 19.

k is in A293698 iff Pi/4 <= k - m*Pi < arctan(2) for some m. We may then verify the following:

If Pi/4 <= k - m*Pi < arctan(2) - 16 + 5*Pi, then k+16 is the next term of A293698.

If arctan(2) - 16 + 5*Pi <= k - m*Pi < 5*Pi/4 - 3, then k+19 is the next term of A293698.

If 5*Pi/4 - 3 <= k - m*Pi < arctan(2), then k+3 is the next term of A293698. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

A293698:= select(i -> floor(tan(i))=1, [$1..1000]):
A293698[2..-1]-A293698[1..-2]; # Robert Israel, Nov 06 2017

Mathematica

rootsp = Flatten[Position[Table[Floor[Tan[i]], {i, 1, 10^6}], 1]];
difp = Differences[rootsp]
(*a(n)=difp[[n]]*)
Differences@ Select[ Range@750, Floor@ Tan@# == 1 &] (* Robert G. Wilson v, Nov 06 2017 *)

Prog

(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

Crossrefs

Cf. A258200, A258007, A293701, A293704, A293698, A293751, A293699, A293702, A293705.

Sequence in context: A293699 A258200 A258007 * A114365 A084559 A272815

Adjacent sequences: A293697 A293698 A293699 * A293701 A293702 A293703

Keyword

nonn

Author

V.J. Pohjola, Oct 16 2017

Status

approved