A276384 Defined by the properties that it starts with 0, and when you successively apply DIFF, RUNS, BISECT, RUNS you get (4,1,3,1) repeated infinitely often.

0, 1, 3, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 23, 25, 27, 29, 31, 33, 34, 36, 38, 40, 42, 44, 45, 47, 49, 51, 53, 55, 57, 58, 60, 62, 64, 66, 68, 69, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 90, 91, 93, 95, 97, 99, 101, 103, 104, 106, 108, 110, 112, 114, 115, 117, 119, 121, 123, 125, 126, 128, 130, 132

Offset: 0

Author

N. J. A. Sloane, Sep 03 2016

Keywords

• nonn

Comments

Here DIFF means take first differences, RUNS means list successive run lengths, and BISECT means take alternate terms.

This agrees with the Beatty sequence for the tribonacci constant (A158919) for n <= 17160 but thereafter is different. In fact A158919(17161) = 31564, whereas a(17161) = 31563.

This arose in an attempt to find recurrences for A158919 and several related sequences. The moral is that without a proof, apparent recurrences are worthless.

Examples

			Seq. 0, 1, 3, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 23, 25, 27, 29, ...
DIFF 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2 ...
RUNS 1, 5, 1, 5, 1, 5, 1, 5, 1, 6, 1, 5, 1, 5, 1, 5, 1, 6, 1, 5, 1, ...
BISECT  5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 5, ...
RUNS 4, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 4, ...
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..40000

Crossrefs

Cf. A158919, A276385.

Programs

Maple

with(transforms): r1:=[]:
for n from 1 to 1000 do r1:=[op(r1), 1,5,1,5,1,5,1,5,1,6,1,5,1,5,1,5,1,6]; od:
r2:=[]: for n from 1 to nops(r1) do if r1[n]=1 then r2:=[op(r2),1]; else for i from 1 to r1[n] do r2:=[op(r2),2]; od: fi: od:
r3:=[0,op(PSUM(r2))]:

Formula

For n >= 1, a(n) = A276385(n)-n.