OFFSET
0,4
COMMENTS
This sequence has similarities with A087734; here we reverse some consecutive bits, there we negate some consecutive bits.
LINKS
FORMULA
EXAMPLE
The first terms, alongside their binary expansion, are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
0 0 0 0
1 1 1 1
2 1 10 1
3 3 11 11
4 1 100 1
5 3 101 11
6 3 110 11
7 7 111 111
8 1 1000 1
9 3 1001 11
10 5 1010 101
11 7 1011 111
12 3 1100 11
13 7 1101 111
14 7 1110 111
15 15 1111 1111
16 1 10000 1
MAPLE
f:= proc(n) local L, nL, i, j, k, r, x;
L:= convert(n, base, 2);
nL:= nops(L);
r:= n;
for i from 1 to nL-1 do
for j from i+1 to nL do
r:= min(r, n + add((L[j-k]-L[i+k])*2^(i+k-1), k=0..j-i));
od od;
r
end proc:
map(f, [$0..100]); # Robert Israel, Aug 13 2024
PROG
(PARI) a(n, base = 2) = { my (d = if (n, digits(n, base), [0])); setbinop((i, j) -> fromdigits(concat([d[1..i-1], Vecrev(d[i..j]), d[j+1..#d]]), base), [1..#d])[1]; }
(Python)
def a(n):
b = bin(n)[2:]
return min(int(b[:i]+b[i:j][::-1]+b[j:], 2) for i in range(len(b)) for j in range(i, len(b)+1))
print([a(n) for n in range(74)]) # Michael S. Branicky, Aug 13 2024
CROSSREFS
KEYWORD
AUTHOR
Rémy Sigrist, Aug 10 2024
STATUS
approved