A309252 - OEIS

%I #22 Aug 21 2019 03:20:01

%S 1,2,5,8,4,7,10,13,16,19,22,11,14,17,20,23,26,29,32,35,38,41,44,47,50,

%T 25,28,31,34,37,40,43,46,49,52,55,58,61,64,67,70,73,76,79,82,85,88,91,

%U 94,97,100,103,106,53,56,59,62,65,68,71,74,77,80,83,86,89,92,95,98,101

%N a(n) is the least number not in the sequence so far and whose absolute difference from a(n-1) is not in the sequence so far, with a(1) = 1 and a(2) = 2.

%C a(n) (mod 3) != 0;

%C a(n) >= n except for n= 5, 12, 26, 54, 110, 222, 446, 894, ...;

%C a(n) < 2n except for n= 4, 11, 25, 53, 109, 221, 445, 893, ...;

%C First occurrence of k or 0 if impossible: 1, 2, 0, 5, 3, 0, 6, 4, 0, 7, 12, 0, 8, 13, 0, 9, 14, 0, 10, 15, 0, 11, 16, 0, 26, 17, 0, 27, 18, 0, ..., .

%e a(3) cannot be 3 since 3-2 = 1 which is a(1), it cannot be 4 since 4-2 = 2 which is a(2), but a(3) can be 5.

%p b:= proc(n) option remember; n in {1, 2} end:

%p a:= proc(n) option remember; local k, t; if n<3 then n

%p       else t:= a(n-1); for k while b(k) or

%p            b(abs(k-t)) do od; b(k):= true; k fi

%p     end:

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 19 2019

%t a[n_] := a[n] = Block[{b = a[n -1], k = 3, s = Array[a, n -1]}, While[ MemberQ[s, k] || MemberQ[s, Abs[b -k]], k++]; k]; a[1] = 1; a[2] = 2; Array[a, 70]

%Y Cf. A001651, A005408.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Jul 18 2019