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A093506 Variation on Golomb's sequence starting with (1,2): a(n)=length of n-th run of consecutive integers with same parity. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A138607 A166014 A199779 * A238980 A082006 A277375

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

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Last modified May 25 16:02 EDT 2017. Contains 287039 sequences.