The On-Line Encyclopedia of Integer Sequences (OEIS)

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A187911

Rank transform of the sequence (1+floor(n*r)), where r=(-1+sqrt(5))/2; complement of A187912.
(history; published version)

#5 by N. J. A. Sloane at Sun Dec 04 19:46:25 EST 2016

MATHEMATICA

(*by _Peter J. C. Moses, _, Mar 15 2011*)

Discussion

Sun Dec 04

19:46

OEIS Server: https://oeis.org/edit/global/2576

#4 by Russ Cox at Fri Mar 30 18:57:21 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Mar 15 2011

Discussion

Fri Mar 30

18:57

OEIS Server: https://oeis.org/edit/global/285

#3 by T. D. Noe at Tue Mar 15 19:37:23 EDT 2011

STATUS

proposed

approved

#2 by Clark Kimberling at Tue Mar 15 17:48:39 EDT 2011

NAME

allocated for Clark KimberlingRank transform of the sequence (1+floor(n*r)), where r=(-1+sqrt(5))/2; complement of A187912.

DATA

1, 3, 4, 5, 7, 8, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 24, 26, 27, 28, 29, 31, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 47, 49, 50, 52, 53, 54, 56, 57, 58, 59, 61, 63, 64, 66, 68, 69, 70, 71, 73, 74, 75, 77, 78, 80, 81, 82, 84, 86, 87, 89, 90, 91, 93, 94, 96, 98, 99, 100, 101, 103, 105, 106, 107, 108, 110, 111, 112, 114, 116, 117, 118, 119

OFFSET

1,2

COMMENTS

See A187224.

MATHEMATICA

See A187224.

r=(-1+5^(1/2))/2;

seqA = Table[1+Floor[r*n], {n, 1, 220}] (*A019446*)

seqB = Table[n, {n, 1, 220}]; (*A000027*)

jointRank[{seqA_,

seqB_}] := {Flatten@Position[#1, {_, 1}],

Flatten@Position[#1, {_, 2}]} &[

Sort@Flatten[{{#1, 1} & /@ seqA, {#1, 2} & /@ seqB}, 1]];

limseqU =

FixedPoint[jointRank[{seqA, #1[[1]]}] &,

jointRank[{seqA, seqB}]][[1]] (*A187911*)

Complement[Range[Length[seqA]], limseqU] (*A187912*)

(*by Peter Moses, Mar 15 2011*)

CROSSREFS

Cf. A187224, A187912.

KEYWORD

allocated

nonn

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Mar 15 2011

STATUS

approved

proposed

#1 by Clark Kimberling at Tue Mar 15 16:20:50 EDT 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved