A363406 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.

3, 9, 13, 17, 23, 27, 33, 37, 43, 47, 51, 57, 61, 67, 71, 75, 81, 85, 91, 95, 99, 105, 109, 115, 119, 125, 129, 133, 139, 143, 149, 153, 157, 163, 167, 173, 177, 183, 187, 191, 197, 201, 207, 211, 215, 221, 225, 231, 235, 241, 245, 249, 255, 259, 265, 269, 273, 279, 283, 289, 293, 297

Offset

1,1

Comments

The first differences could be related to A004641. (From Bradley Klee via Seqfan list.)

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

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

Starting with L = 1,2,3,4,..., the values of j, k, and a(n) are computed (and L is updated) as follows:
  n  j  k  a(n)                            L
  =  =  =  ====  ======================================================
  -  -  -    -   1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
  1  1  2    3       3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
  2  3  6    9         4,5,  7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
  3  4  9   13           5,  7,8,  10,11,12,13,14,15,16,17,18,19,20,...
  4  5 12   17               7,8,  10,11,   13,14,15,16,17,18,19,20,...
  5  7 16   23                 8,  10,11,   13,14,15,   17,18,19,20,...
  6  8 19   27                     10,11,   13,14,15,   17,18,   20,...

Prog

(MATLAB)
function a = A363406( max_n )
    L = [1:max_n+2];
    for n = 1:max_n
        a(n) = L(1) + L(L(1)+1); l = L(end);
        L = [L(2:L(1)) L(L(1)+2:end)];
        L = [L 1+l:1+l+L(1)];
    end
end % Thomas Scheuerle, Jun 01 2023
(Python)
from itertools import islice
def agen():  # generator of terms
    L = list(range(1, 10))
    while True:
        j = L[0]
        k = L[j]
        yield j + k  # an
        L.remove(j)
        L.remove(k)
        L.extend(list(range(L[-1]+1, L[-1]+7)))
print(list(islice(agen(), 62))) # Michael S. Branicky, Dec 20 2024

Crossrefs

Cf. A004641.

Sequence in context: A345460 A239320 A243656 * A240108 A163595 A088090

Adjacent sequences: A363403 A363404 A363405 * A363407 A363408 A363409

Keyword

nonn

Author

Ali Sada and David James Sycamore, May 31 2023

Status

approved