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A285679 Positions of 2 in A285677. 4
3, 5, 10, 12, 17, 22, 24, 29, 31, 36, 41, 43, 48, 53, 55, 60, 62, 67, 72, 74, 79, 81, 86, 91, 93, 98, 103, 105, 110, 112, 117, 122, 124, 129, 134, 136, 141, 143, 148, 153, 155, 160, 162, 167, 172, 174, 179, 184, 186, 191, 193, 198, 203, 205, 210, 212, 217 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A 3-way partition of the positive integers, by positions of 0, 1, 2 in A285677:

A285678: positions of 0; slope t = (4+sqrt(5))/2;

A182761: positions of 1; slope u = (7-sqrt(5))/2;

A285679: positions of 2; slope v = (1+3*sqrt(5))/2;

where 1/t + 1/u + 1/v = 1.

Conjecture:  a(n) - a(n-1) is in {2,5} for n>=2.

See A285683 for a proof of this conjecture. - Michel Dekking, Oct 09 2018

a(n) = A285683(n-1)  for n>1, see A285683 for a proof. - Michel Dekking, Oct 09 2018

LINKS

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

FORMULA

a(n) = 3*floor((n-1)*phi) - n + 4

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] ; (* A003849 *)

w = StringJoin[Map[ToString, s]]

w1 = StringReplace[w, {"0010" -> "2"}]

st = ToCharacterCode[w1] - 48; (* A285677 *)

Flatten[Position[st, 0]];  (* A285678 *)

Flatten[Position[st, 1]];  (* A182761 *)

Flatten[Position[st, 2]];  (* A285679 *)

CROSSREFS

Cf. A003849, A284620, A285678, A182761, A285679.

Sequence in context: A212537 A047389 A263652 * A093661 A080561 A266663

Adjacent sequences:  A285676 A285677 A285678 * A285680 A285681 A285682

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 11 2017

STATUS

approved

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Last modified February 22 02:13 EST 2019. Contains 320381 sequences. (Running on oeis4.)