

A086398


a(1)=1; a(n)=a(n1)+2 if n is in the sequence; a(n)=a(n1)+2 if n and (n1) are not in the sequence; a(n)=a(n1)+4 if n is not in the sequence but (n1) is in the sequence.


3



1, 5, 7, 9, 11, 15, 17, 21, 23, 27, 29, 33, 35, 37, 39, 43, 45, 49, 51, 53, 55, 59, 61, 65, 67, 69, 71, 75, 77, 81, 83, 85, 87, 91, 93, 97, 99, 103, 105, 109, 111, 113, 115, 119, 121, 125, 127, 129, 131, 135, 137, 141, 143, 147, 149, 153, 155, 157, 159, 163, 165, 169
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OFFSET

1,2


COMMENTS

Conjecture: the positions of 1 in the fixed point of the morphism 0 > 10, 1 > 1000, and 1 < n*(1 + sqrt(3))  a(n) < 4 for n>=1; see A285301.  Clark Kimberling, Apr 25 2017


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = (1+sqrt(3))*n + O(1).


MATHEMATICA

s = Nest[Flatten[# /. {0 > {1, 0}, 1 > {1, 0, 0, 0}}] &, {0}, 10]; (* A285301 *)
Flatten[Position[s, 0]]; (* A285302 *)
Flatten[Position[s, 1]]; (* A086398 *)


PROG

(PARI) x=1; y=2; z=2; t=4; an[1]=x; for(n=2, 100, an[n]=if(setsearch(Set(vector(n1, i, a(i))), n), a(n1)+y, if(setsearch(Set(vector(n1, i, a(i))), n1), a(n1)+t, a(n1)+z)))


CROSSREFS

Cf. A086377, A285301, A285302.
Sequence in context: A314375 A309747 A080384 * A023380 A076190 A028885
Adjacent sequences: A086395 A086396 A086397 * A086399 A086400 A086401


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Sep 13 2003


STATUS

approved



