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A356993 a(n) = b(n - b(n - b(n - b(n)))) for n >= 2, where b(n) = A356988(n). 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A107320 A095186 A265340 * A189631 A101402 A156251
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Sep 09 2022
STATUS
approved

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Last modified June 22 12:55 EDT 2024. Contains 373571 sequences. (Running on oeis4.)