A356993 a(n) = b(n - b(n - b(n - b(n)))) for n >= 2, where b(n) = A356988(n).

1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 10, 11, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 16, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 23, 24, 25, 26, 27, 28, 29, 29, 29, 29

Offset

2,5

Comments

The sequence is slow, that is, for n >= 2, a(n+1) - a(n) is either 0 or 1. The sequence is unbounded.

The line graph of the sequence {a(n)} thus consists of a series of plateaus (where the value of the ordinate a(n) remains constant as n increases) joined by lines of slope 1.

The sequence of plateau heights beginning 3, 4, 5, 7, 8, 11, 13, 18, 21, 29, 34, 47, 55, ..., consists of alternating Fibonacci numbers A000045 and Lucas numbers A000032.

Links

Table of n, a(n) for n=2..87.

Peter Bala, Notes on A356993

Formula

a(2) = a(3) = a(4) = a(5) = 1 and then for k >= 3 there holds

a(3*F(k) + j) = F(k) for 0 <= j <= F(k-1) (local plateau)

a(L(k+1) + j) = F(k) + j for 0 <= j <= F(k-2) (ascent to plateau of height L(k-1))

a(4*F(k) + j) = L(k-1) for 0 <= j <= F(k-1) (local plateau)

a(4*F(k) + F(k-1) + j) = L(k-1) + j for 0 <= j <= F(k-3) (ascent to next plateau of height F(k+1)).

Maple

# b(n) = A356988
b := proc(n) option remember; if n = 1 then 1 else n - b(b(n - b(b(b(n-1))))) end if; end proc:
seq( b(n - b(n - b(n - b(n)))), n = 2..100 );

Crossrefs

Cf. A000032, A000045, A000285, A022087, A356988, A356991 - A356999.

Sequence in context: A095186 A265340 A373503 * A189631 A101402 A156251

Adjacent sequences: A356990 A356991 A356992 * A356994 A356995 A356996

Keyword

nonn,easy

Author

Peter Bala, Sep 09 2022

Status

approved