A093506 Variation on Golomb's sequence starting with (1,2): a(n)=length of n-th run of consecutive integers with same parity.

1, 2, 4, 3, 5, 7, 9, 6, 8, 10, 11, 13, 15, 17, 19, 12, 14, 16, 18, 20, 22, 24, 21, 23, 25, 27, 29, 31, 33, 35, 37, 26, 28, 30, 32, 34, 36, 39, 41, 43, 45, 47, 49, 51, 53, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 58, 60, 62, 64, 66, 68, 70

Offset

1,2

Comments

A permutation of positive integers.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

Does a(n)=n+o(n)? Does a(n)=n for infinitely many values of n?

Example

Runs of odd or even terms are : (1),(2,4),(3,5,7,9),(6,8,10),(11,13,15,17,19),...and computing the number of integers in each run we get : 1,2,4,3,5,...the sequence itself.

Prog

(GNU bc)
maxarray=2^16;
print oe[1]=a[1]=1, ", ", a[2]=2, ", ", oe[k=0]=a[p=n=3]=4, ", ";
for(max=100; p<maxarray&&n<max; p++) {
    for(i=0*k=!k; i<a[p]&&n<max; i++) {
        an=oe[k]+=2;
        if (++n<maxarray) a[n]=an;
        print an, ", "
    };
}; /* Carl R. White, Jan  05 2013 */
(Haskell)
a093506 n = a093506_list !! (n-1)
a093506_list = 1 : 2 : f 1 [1] [3, 5..] [4, 6..]
   where f 0 (z:zs) odds evens = orun ++ f 1 (zs ++ orun) odds' evens
           where (orun, odds') = splitAt z odds
         f 1 (z:zs) odds evens = erun ++ f 0 (zs ++ erun) odds evens'
           where (erun, evens') = splitAt z evens
-- Reinhard Zumkeller, Jan 06 2013

Crossrefs

Cf. A001462.

Cf. A187790 (inverse), A187792 (fixed points).

Sequence in context: A357527 A348357 A199779 * A307485 A238980 A327143

Adjacent sequences: A093503 A093504 A093505 * A093507 A093508 A093509

Keyword

nonn

Author

Benoit Cloitre, May 14 2004

Extensions

Sequence corrected by Carl R. White, Jan 06 2013

Status

approved