A363406 - OEIS

%I #42 Dec 20 2024 12:36:19

%S 3,9,13,17,23,27,33,37,43,47,51,57,61,67,71,75,81,85,91,95,99,105,109,

%T 115,119,125,129,133,139,143,149,153,157,163,167,173,177,183,187,191,

%U 197,201,207,211,215,221,225,231,235,241,245,249,255,259,265,269,273,279,283,289,293,297

%N Start with list L = 1,2,3,4,.... For n = 1,2,3,..., iterate as follows: let j = L(1) and k = L(j+1), get a(n) = j + k, and remove j and k from L.

%C The first differences could be related to A004641. (From _Bradley Klee_ via Seqfan list.)

%C The first differences appear to always be 4 or 6. The relationship A363406(n) - A363406(n-1) = 6 iff A004641(n-1) = 1 first fails at n = 50. - _Michael S. Branicky_, Dec 20 2024

%H Michael S. Branicky, <a href="/A363406/b363406.txt">Table of n, a(n) for n = 1..10000</a>

%e Starting with L = 1,2,3,4,..., the values of j, k, and a(n) are computed (and L is updated) as follows:

%e   n  j  k  a(n)                            L

%e   =  =  =  ====  ======================================================

%e   -  -  -    -   1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...

%e   1  1  2    3       3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...

%e   2  3  6    9         4,5,  7,8,9,10,11,12,13,14,15,16,17,18,19,20,...

%e   3  4  9   13           5,  7,8,  10,11,12,13,14,15,16,17,18,19,20,...

%e   4  5 12   17               7,8,  10,11,   13,14,15,16,17,18,19,20,...

%e   5  7 16   23                 8,  10,11,   13,14,15,   17,18,19,20,...

%e   6  8 19   27                     10,11,   13,14,15,   17,18,   20,...

%o (MATLAB)

%o function a = A363406( max_n )

%o     L = [1:max_n+2];

%o     for n = 1:max_n

%o         a(n) = L(1) + L(L(1)+1); l = L(end);

%o         L = [L(2:L(1)) L(L(1)+2:end)];

%o         L = [L 1+l:1+l+L(1)];

%o     end

%o end % _Thomas Scheuerle_, Jun 01 2023

%o (Python)

%o from itertools import islice

%o def agen():  # generator of terms

%o     L = list(range(1, 10))

%o     while True:

%o         j = L[0]

%o         k = L[j]

%o         yield j + k  # an

%o         L.remove(j)

%o         L.remove(k)

%o         L.extend(list(range(L[-1]+1, L[-1]+7)))

%o print(list(islice(agen(), 62))) # _Michael S. Branicky_, Dec 20 2024

%Y Cf. A004641.

%K nonn

%O 1,1

%A _Ali Sada_ and _David James Sycamore_, May 31 2023