A283207 a(n) = a(floor(n/a(n-1))) + a(floor(n/a(n-2))) with a(1) = a(2) = 2.

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

Links

Altug Alkan, Table of n, a(n) for n = 1..10000

Altug Alkan, Alternative Graph of A283207

Altug Alkan, Line plot of (a(floor(n/a(n-1))), a(floor(n/a(n-2)))) for n <= 2^15

Rémy Sigrist, Scatterplot of the first 2^34 terms

Rémy Sigrist, Line plot of (a(floor(n/a(n-1))), a(floor(n/a(n-2)))) for n <= 12855108032

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

Cf. A005185, A130535.

Sequence in context: A071805 A063511 A334789 * A164717 A164715 A164632

Adjacent sequences: A283204 A283205 A283206 * A283208 A283209 A283210

Keyword

nonn

Author

Altug Alkan, Mar 03 2017

Status

approved