A394219 - OEIS

%I #19 Apr 06 2026 09:55:24

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

%T 15,15,16,16,17,18,18,19,20,20,21,21,22,23,23,24,25,25,26,26,27,27,28,

%U 28,29,29,30,30,31,31,32,32,33,33,34,34,34,35,35,36,36,36,37,37,37,38,38,39,39,39,40

%N Earliest monotonic sequence satisfying a(1)=1 and a(a(n)+a(n-1)+a(n-2)+a(n-3)) = 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.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a394/A394219.java">Java program</a> (github)

%F a(1)=1, a(2)=2, a(3)=2, a(4)=2, a(5)=3, a(6)=3, a(7)=4, a(8)=4.

%F For n >= 2,

%F a(4*n)   = a(n-3) + a(n-2) + a(n-1) + a(n) + 1 + c0(n),

%F a(4*n+1) = a(n-2) + a(n-1) + a(n) + a(n+1) + c1(n),

%F a(4*n+2) = a(n-2) + a(n-1) + a(n) + a(n+1) + c2(n),

%F a(4*n+3) = a(n-1) + a(n) + a(n+1) + a(n+2) - 1 + c3(n),

%F where c0,c1,c2,c3 are four 0-1 correction sequences with explicit 4-adic recurrences.

%Y Cf. A001462, A394217, A394218.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Mar 12 2026