A087851 a(n) = abs(a(n-1) - floor(n*phi)), where phi=(1+sqrt(5))/2, with a(1) = a(2) = 1.

1, 1, 3, 3, 5, 4, 7, 5, 9, 7, 10, 9, 12, 10, 14, 11, 16, 13, 17, 15, 18, 17, 20, 18, 22, 20, 23, 22, 24, 24, 26, 25, 28, 27, 29, 29, 30, 31, 32, 32, 34, 33, 36, 35, 37, 37, 39, 38, 41, 39, 43, 41, 44, 43, 45, 45, 47, 46, 49, 48, 50, 50, 51, 52, 53, 53, 55, 55, 56, 57, 57, 59, 59

Offset

1,3

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(1) = a(2) = 1; for n > 2, a(n) = |a(n-1)-floor(n*phi)|. - Joshua Zucker, Jun 16 2007

Mathematica

Join[{1}, Block[{n = 2}, NestList[Abs[# - Floor[++n*GoldenRatio]] &, 1, 100]]] (* Paolo Xausa, May 12 2024 *)

Prog

(True BASIC)
61 LET gm=(1+Sqr(5))/2
70 DIM q0(0 to 4000)
80 LET q0(1)=1
90 LET q0(2)=1
91 FOR n = 3 to 201
92 LET q0(n)=Abs(q0(n-1)-int(n*gm))
93 NEXT n
100 SET MODE "color"
110 SET WINDOW 0, 1024, 0, 750
302 PRINT" by Roger L. Bagula Oct 07 2003 "
381 OPEN #1: name "CM1:simple_data", create newold, org text
390 FOR x=1 to 200
391 PRINT #1: q0(x); ", ";
392 PRINT q0(x);
393 NEXT x
394 CLOSE #1
460 END

Crossrefs

Cf. A087852, A087853.

A129229 is a very similar sequence.

Sequence in context: A075795 A058268 A341729 * A332932 A087852 A087853

Adjacent sequences: A087848 A087849 A087850 * A087852 A087853 A087854

Keyword

nonn,easy

Author

Roger L. Bagula, Oct 08 2003

Extensions

Edited by N. J. A. Sloane, Jun 18 2007

Status

approved