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A283207
a(n) = a(floor(n/a(n-1))) + a(floor(n/a(n-2))) with a(1) = a(2) = 2.
4
2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 6, 4, 6, 6, 4, 8, 6, 6, 8, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
OFFSET
1,1
COMMENTS
For the first 10^6 terms, the maximum value of a(n) is 64 and the values of b(n) = least k such that a(k) = 2*n are 1, 3, 13, 12, 105, 97, 126, 96, 1681, 1552, 1746, 1537, 1734, 1926, 4050, 1536, 53793, 49665, 53890, 49185, 53862, 57024, 55616, 49153, 55488, 55302, 81249, 61446, 83619, 115214, 162000, 49152; note that b(2^n) = 3*2^((n+2)*(n-1)/2) for n = 1 to 5.
This sequence is a_{1,2}(n) where a_{r,s}(n) = a_{r,s}(floor(n/a_{r,s}(n-r))) + a_{r,s}(floor(n/a_{r,s}(n-s))) with a_{r,s}(n) = 2 for n <= s (r < s). - Altug Alkan, Jun 28 2020
EXAMPLE
a(5) = 4 because a(5) = a(floor(5/a(4))) + a(floor(5/a(3))) = a(floor(5/4)) + a(floor(5/4)) = a(1) + a(1) = 4.
MAPLE
A:= Vector(100):
A[1]:= 2: A[2]:= 2:
for n from 3 to 100 do A[n]:= A[floor(n/A[n-1])] + A[floor(n/A[n-2])] od:
convert(A, list); # Robert Israel, Jun 23 2020
MATHEMATICA
a[1] = a[2] = 2; a[n_] := a[n] = a[Floor[n/a[n - 1]]] + a[Floor[n/a[n - 2]]]; Array[a, 120] (* Michael De Vlieger, Mar 06 2017 *)
PROG
(PARI) a=vector(100); a[1]=a[2]=2; for(n=3, #a, a[n]=a[n\a[n-1]]+a[n\a[n-2]]); a
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A283207(n):
return 2 if n <= 2 else A283207(n//A283207(n-1)) + A283207(n//A283207(n-2)) # Chai Wah Wu, Jun 23 2020
CROSSREFS
Sequence in context: A071805 A063511 A334789 * A164717 A164715 A164632
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 03 2017
STATUS
approved