OFFSET
1,2
COMMENTS
Consider an alternate complexity measure b(n) which gives the minimum number of 1's necessary to build n using +, -, *, and / (where this additional operation is strict integer division, defined only for n/d where d|n). It turns out that b(n) coincides with a(n) for all n up to 50221174, see A348069. - Glen Whitney, Sep 23 2021
In respect of the previous comment: when creating A362471, where repunits are allowed, we found a difference if we allowed n/d with noninteger (intermediate) results. So, see also A362626. - Peter Munn, Apr 29 2023
LINKS
Janis Iraids, Table of n, a(n) for n = 1..10000
Juris Cernenoks, Janis Iraids, Martins Opmanis, Rihards Opmanis and Karlis Podnieks, Integer Complexity: Experimental and Analytical Results II, arXiv:1409.0446 [math.NT], 2014.
Janis Iraids, A C program to compute the sequence
J. Iraids, K. Balodis, J. Cernenoks, M. Opmanis, R. Opmanis and K. Podnieks, Integer Complexity: Experimental and Analytical Results. arXiv preprint arXiv:1203.6462 [math.NT], 2012. - From N. J. A. Sloane, Sep 22 2012
EXAMPLE
PROG
(Python)
from functools import cache
@cache
def f(m):
if m == 0: return set()
if m == 1: return {1}
out = set()
for j in range(1, m//2+1):
for x in f(j):
for y in f(m-j):
out.update([x + y, x * y])
if x != y: out.add(abs(x-y))
return out
def aupton(terms):
tocover, alst, n = set(range(1, terms+1)), [0 for i in range(terms)], 1
while len(tocover) > 0:
for k in f(n) - f(n-1):
if k <= terms:
alst[k-1] = n
tocover.discard(k)
n += 1
return alst
print(aupton(77)) # Michael S. Branicky, Sep 28 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jens Voß, Dec 30 2003
STATUS
approved