A268182 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

Table of n, a(n) for n=1..59.

Index entries for sequences that are permutations of the natural numbers

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

PROG

(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

CROSSREFS

Cf. A168616.

Sequence in context: A371418 A340406 A257881 * A094339 A317788 A375963

Adjacent sequences: A268179 A268180 A268181 * A268183 A268184 A268185

KEYWORD

nonn

AUTHOR

Toby Chamberlain, Jan 28 2016

STATUS

approved