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A086398 a(1)=1; a(n)=a(n-1)+2 if n is in the sequence; a(n)=a(n-1)+2 if n and (n-1) are not in the sequence; a(n)=a(n-1)+4 if n is not in the sequence but (n-1) 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 (list; graph; refs; listen; history; text; internal format)
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(n-1, i, a(i))), n), a(n-1)+y, if(setsearch(Set(vector(n-1, i, a(i))), n-1), a(n-1)+t, a(n-1)+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

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Last modified November 26 07:49 EST 2020. Contains 338632 sequences. (Running on oeis4.)