A276385 - OEIS

%I #17 Sep 04 2016 13:46:58

%S 2,5,8,11,14,17,19,22,25,28,31,34,36,39,42,45,48,51,53,56,59,62,65,68,

%T 70,73,76,79,82,85,88,90,93,96,99,102,105,107,110,113,116,119,122,124,

%U 127,130,133,136,139,141,144,147,150,153,156,159,161,164,167,170,173,176,178,181,184,187,190,193

%N 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.

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

%C 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.

%C 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.

%H N. J. A. Sloane, <a href="/A276385/b276385.txt">Table of n, a(n) for n = 1..40000</a>

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

%e Seq. 2, 5, 8, 11, 14, 17, 19, 22, 25, 28, 31, 34, 36, 39, 42, 45, 48, 51, 53, 56, ...

%e 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, ...

%e 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, ...

%e 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, ...

%e RUNS 4, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 4, ...

%p with(transforms): r1:=[]:

%p 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:

%p 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:

%p r3:=[2, op(map(x->x+2,PSUM(r2)))]:

%Y Cf. A140099, A158919, A276384.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Sep 03 2016