OFFSET
1,2
REFERENCES
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, p. 374.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint 2016.
Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585.
FORMULA
a(n) = A123753(n-1) - (n-1) mod 2. - Peter Luschny, Nov 30 2017
MAPLE
A054248 := proc(n) local i, j; option remember; if n<=2 then n else j := 10^10; for i from 1 to n-1 do if A054248(i)+A054248(n-i) < j then j := A054248(i)+A054248(n-i); fi; od; n+j; fi; end;
# second Maple program:
a:= proc(n) option remember; `if`(n<3, n,
n + min(seq(a(k)+a(n-k), k=1..n/2)))
end:
seq(a(n), n=1..80); # Alois P. Heinz, Aug 29 2015
MATHEMATICA
a[n_] := n + n IntegerLength[n, 2] - 2^IntegerLength[n, 2] + Mod[n, 2];
Table[a[n], {n, 1, 54}] (* Peter Luschny, Dec 02 2017 *)
PROG
(Python)
def A054248(n):
s, i, z = n - (n-1) % 2, n-1, 1
while 0 <= i: s += i; i -= z; z += z
return s
print([A054248(n) for n in range(1, 55)]) # Peter Luschny, Nov 30 2017
(Python)
def A054248(n): return n*(1+(m:=(n-1).bit_length()))-(1<<m)+(n&1) # Chai Wah Wu, Mar 29 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 04 2000
STATUS
approved