OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
Shalosh B. Ekhad, Everything About Formulas Representing Integers Using Additions and Multiplication for integers from 1 to 8000.
Edinah K. Ghang, Doron Zeilberger, Zeroless Arithmetic: Representing Integers ONLY using ONE, arXiv:1303.0885 [math.CO], 2013
FORMULA
a(n) = 2*A005245(n)-1.
EXAMPLE
a(3) = 5 because for n = 3, the minimum is length = 5, formula = "11+1+" or "111++".
MAPLE
with(numtheory):
a:= proc(n) option remember;
1+ `if`(n=1, 0, min(seq(a(i)+a(n-i), i=1..n/2),
seq(a(d)+a(n/d), d=divisors(n) minus {1, n})))
end:
seq(a(n), n=1..100); # Alois P. Heinz, Mar 07 2013
MATHEMATICA
a[n_] := a[n] = 1 + If[n == 1, 0, Min[Join[Table[a[i] + a[n-i], {i, 1, n/2}], Table[a[d] + a[n/d], {d, Divisors[n] ~Complement~ {1, n}}]]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 01 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Mar 06 2013
STATUS
approved