A394218 - OEIS

%I #20 Apr 06 2026 09:55:20

%S 1,2,2,2,3,4,5,5,6,6,6,7,7,8,8,9,10,11,12,13,13,14,15,15,16,16,17,17,

%T 17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,26,26,27,28,29,

%U 30,31,32,33,34,35,36,37,37,38,39,39,40,41,41,42,43,43,44,45,45,46,46,47,47,48,48,49,49

%N Earliest monotonic sequence satisfying a(1)=1 and a(a(n)+a(n-1)+a(n-2)) = n for n>=1 (with a(k)=0 for k<=0).

%H Benoit Cloitre, <a href="https://arxiv.org/abs/2604.02404">Almost Golomb Sequences</a>, arXiv:2604.02404 [math.NT], 2026.

%F a(1)=1, a(2)=2, a(3)=2, a(4)=2, a(5)=3, and for k >= 2,

%F a(3k) = a(k-2) + a(k-1) + a(k) + 1 + c(k-1),

%F a(3k+1) = a(k-1) + a(k) + a(k+1),

%F a(3k+2) = a(k) + a(k+1) + a(k+2) - 1 - c(k),

%F where c(m)=0 for m<5, c(5)=1, and for j >= 2: c(3j) = c(j-1), c(3j+1) = c(3j+2) = c(j).

%Y Cf. A001462, A394217, A394219.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Mar 12 2026