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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.
4
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 03 2016
STATUS
approved