

A093506


Variation on Golomb's sequence starting with (1,2): a(n)=length of nth 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
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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 !! (n1)
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



