A352840 a(1) = 0; a(2) = 1; thereafter a(n) = a(n-1)/2 if a(n-1) is even, otherwise a(n) = a(n-1) + a((n-1)-a(n-1)).

0, 1, 1, 2, 1, 3, 4, 2, 1, 3, 7, 9, 10, 5, 6, 3, 13, 15, 16, 8, 4, 2, 1, 3, 7, 22, 11, 14, 7, 9, 13, 28, 14, 7, 18, 9, 20, 10, 5, 12, 6, 3, 8, 4, 2, 1, 3, 7, 13, 22, 11, 23, 30, 15, 20, 10, 5, 28, 14, 7, 37, 40, 20, 10, 5, 12, 6, 3, 8, 4, 2, 1, 3, 7, 13, 53

Offset

1,4

Links

Gavin Lupo, Table of n, a(n) for n = 1..10000

Example

a(1)=0.
a(2)=1.
1 is odd, so a(3) = a(2) + a(2-a(2)) = a(2) + a(2-1) = a(2) + a(1) = 1 + 0 = 1.
1 is odd, so a(4) = a(3) + a(3-a(3)) = a(3) + a(3-1) = a(3) + a(2) = 1 + 1 = 2.
2 is even, so a(5) = a(4)/2 = 2/2 =  1.
Continuing, we get
   n                           a(n)
   -                           ----
   1                             0
   2                             1
   3      1 + a(1)      1 + 0 =  1
   4      1 + a(2)      1 + 1 =  2
   5      a(4) / 2      2 / 2 =  1
   6      1 + a(4)      1 + 2 =  3
   7      3 + a(3)      3 + 1 =  4
   8      a(7) / 2      4 / 2 =  2
   9      a(8) / 2      2 / 2 =  1
  10      1 + a(8)      1 + 2 =  3
  11      3 + a(7)      3 + 4 =  7
  12      7 + a(4)      7 + 2 =  9

Prog

(Python)
result = [0, 1]
iterations = 100
for i in range(1, iterations):
    if result[i]%2 == 0:
        result.append(result[i] // 2)
    else:
        result.append(result[i] + result[i - result[i]])
print(result, end='', sep=' ')
(MATLAB)
result = [0 1];
iterations = 100;
for i = 2:iterations
    if mod(result(i), 2) == 0
        result(i+1) = int32(result(i)/2);
    else
        result(i+1) = (result(i) + result(i - result(i)));
    end
end

Crossrefs

Cf. A350129.

Sequence in context: A229287 A286539 A004741 * A133923 A347296 A341231

Adjacent sequences: A352837 A352838 A352839 * A352841 A352842 A352843

Keyword

nonn,look,easy

Author

Gavin Lupo, Apr 05 2022

Status

approved