A394218 - OEIS

A394218

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).

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

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OFFSET

1,2

LINKS

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

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

FORMULA

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

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

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

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

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).