A363083 - OEIS

%I #26 May 21 2023 23:33:37

%S 1,1,2,1,3,2,5,3,-2,-5,-3,2,-1,1,0,1,1,2,3,5,2,7,5,-2,3,1,4,3,7,4,-3,

%T -7,-4,3,-1,2,1,3,4,1,5,4,9,5,14,9,-5,-14,-9,5,-4,-9,-5,4,-1,3,2,5,7,

%U 2,9,7,-2,5,3,8,5,13,8,-5,-13,-8,5,-3,2,-1,1,0

%N a(0)=a(1)=1. For n>1, if the number of occurrences of a(n-1) is less than abs(a(n-1)), then a(n)=a(n-1)-a(n-2). Otherwise, a(n)=a(n-1)+a(n-2).

%H Gavin Lupo, <a href="/A363083/b363083.txt">Table of n, a(n) for n = 0..50000</a>

%H Gavin Lupo, <a href="/A363083/a363083.png">Image of the first 100000 terms.</a>

%H Gavin Lupo, <a href="/A363083/a363083_1.png">Image of the first 1000000 terms.</a>

%H Gavin Lupo, <a href="/A363083/a363083_2.png">Image of the first 10000000 terms.</a>

%e a(0) = 1

%e a(1) = 1

%e a(2) = 2. Two 1's in the list so far.    2 > abs(1).   1 + 1 = 2.

%e a(3) = 1. One 2 in the list so far.      1 < abs(2).   2 - 1 = 1.

%e a(4) = 3. Three 1's in the list so far.  3 > abs(1).   1 + 2 = 3.

%o (Python)

%o from itertools import islice

%o from collections import Counter

%o def agen(): # generator of terms

%o     anprev, an, c = 1, 1, Counter([1])

%o     yield 1

%o     while True:

%o         yield an

%o         c[an] += 1

%o         anprev, an = an, an-anprev if c[an] < abs(an) else an+anprev

%o print(list(islice(agen(), 80))) # _Michael S. Branicky_, May 18 2023

%Y Cf. A329985, A362746, A362890, A363086.

%K sign,easy,look

%O 0,3

%A _Gavin Lupo_, May 18 2023