A394219 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).

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

Offset

1,2

Links

Table of n, a(n) for n=1..80.

Benoit Cloitre, Almost Golomb Sequences, arXiv:2604.02404 [math.NT], 2026.

Sean A. Irvine, Java program (github)

Formula

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

For n >= 2,

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

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

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

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

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

Crossrefs

Cf. A001462, A394217, A394218.

Sequence in context: A025795 A219610 A194161 * A051066 A029159 A029099

Adjacent sequences: A394216 A394217 A394218 * A394220 A394221 A394222

Keyword

nonn

Author

Benoit Cloitre, Mar 12 2026

Status

approved