A268182 A solution to a(n+1) in {a(n)+2, a(n)-2, a(n)*2, a(n)/2} which is a rearrangement of the natural numbers.

2, 1, 3, 6, 4, 8, 10, 5, 7, 9, 11, 22, 20, 18, 16, 14, 12, 24, 26, 13, 15, 17, 19, 21, 23, 25, 27, 54, 52, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28, 56, 58, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59

Offset: 1

Author

Toby Chamberlain, Jan 28 2016

Keywords

• nonn

Comments

Use algorithm: when a(n)=2k+1 2k+1 -> 4k+2, 4k, 4k-2, 4k-4, ...-> 2k+2 -> *2-> 4k+4 +2-> 4k+6 -> /2-> 2k+3, 2k+5, +2... ->4k+7. This covers all numbers between 2k+1 and 4k+7 and then the algorithm can be reapplied.

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A168616.

Programs

PARI

{get_next_stage(v) = local(k = (v[#v] - 1)/2);
forstep(m = 2*v[#v], 2*k + 2, -2, v = concat(v, m));
v = concat(v, [2*v[#v], 4*k + 6]);
forstep(m = v[#v]/2, 4*k + 7, 2, v = concat(v, m)); v}
a = [2, 1, 3]; \\ code assumes last entry here is odd.
\\ n-th call to function returns 2^(n + 2) more terms
while (#a < 59, a = get_next_stage(a)); a \\ Rick L. Shepherd, May 21 2016

Formula

a(n) = n if and only if n is a positive term of A168616. Also, for j > 2, a(n) < a(2^j - 5) if and only if n < 2^j - 5. - Rick L. Shepherd, May 22 2016