A276385 Defined by the properties that it starts with 2, and when you successively apply DIFF, RUNS, BISECT, RUNS you get (4,1,3,1) repeated infinitely often.

2, 5, 8, 11, 14, 17, 19, 22, 25, 28, 31, 34, 36, 39, 42, 45, 48, 51, 53, 56, 59, 62, 65, 68, 70, 73, 76, 79, 82, 85, 88, 90, 93, 96, 99, 102, 105, 107, 110, 113, 116, 119, 122, 124, 127, 130, 133, 136, 139, 141, 144, 147, 150, 153, 156, 159, 161, 164, 167, 170, 173, 176, 178, 181, 184, 187, 190, 193

Offset

1,1

Comments

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

This agree with the Beatty sequence for 1+t, where t is the tribonacci constant (A140099) for n <= 17160 but thereafter is different. In fact A140099(17161) = 48725, whereas a(17161) = 48724.

This arose in an attempt to find recurrences for A140099 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 = 1..40000

Formula

For n >= 1, a(n) = A276384(n)+n.

Example

Seq. 2, 5, 8, 11, 14, 17, 19, 22, 25, 28, 31, 34, 36, 39, 42, 45, 48, 51, 53, 56, ...
DIFF 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, ...
RUNS 5, 1, 5, 1, 5, 1, 5, 1, 6, 1, 5, 1, 5, 1, 5, 1, 6, 1, 5, 1, 5, 1, 5, 1, 5, 1, ...
BISECT  5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 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), 5, 1, 5, 1, 5, 1, 5, 1, 6, 1, 5, 1, 5, 1, 5, 1, 6, 1]; od:
r2:=[]: for n from 1 to nops(r1) do if r1[n]=1 then r2:=[op(r2), 2]; else for i from 1 to r1[n] do r2:=[op(r2), 3]; od: fi: od:
r3:=[2, op(map(x->x+2, PSUM(r2)))]:

Crossrefs

Cf. A140099, A158919, A276384.

Sequence in context: A055048 A045930 A140099 * A109232 A064718 A190336

Adjacent sequences: A276382 A276383 A276384 * A276386 A276387 A276388

Keyword

nonn

Author

N. J. A. Sloane, Sep 03 2016

Status

approved