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

0,3

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.

Links

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

Formula

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

Example

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, ...

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))]:

Crossrefs

Cf. A158919, A276385.

Sequence in context: A272915 A094391 A158919 * A329827 A182765 A246407

Adjacent sequences: A276381 A276382 A276383 * A276385 A276386 A276387

Keyword

nonn

Author

N. J. A. Sloane, Sep 03 2016

Status

approved