A187330 -id:A187330 - cp's OEIS frontend

A187339 a(n) = floor((7+sqrt(5))*n/4); complement of A187330.

2, 4, 6, 9, 11, 13, 16, 18, 20, 23, 25, 27, 30, 32, 34, 36, 39, 41, 43, 46, 48, 50, 53, 55, 57, 60, 62, 64, 66, 69, 71, 73, 76, 78, 80, 83, 85, 87, 90, 92, 94, 96, 99, 101, 103, 106, 108, 110, 113, 115, 117, 120, 122, 124, 126, 129, 131, 133, 136, 138, 140, 143, 145

Offset: 1

Clark Kimberling, Mar 08 2011

nonn

A187339 and A187330 are a pair of Beatty sequences.

Cf. A187330.

Table[Floor[((7+5^(1/2))/4)n], {n,1,120}]

a(n)=floor((7+sqrt(5))*n/4).

A187907 Rank transform of the sequence floor((4 - sqrt(5))*n); complement of A187908.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 13, 15, 16, 19, 20, 23, 24, 26, 28, 30, 32, 34, 36, 38, 40, 41, 43, 46, 48, 49, 51, 53, 55, 57, 59, 61, 63, 64, 66, 68, 71, 73, 74, 76, 78, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 139, 141, 143, 145, 147, 149, 151, 153, 155

Offset: 1

Clark Kimberling, Mar 15 2011

nonn

See A187224. A187232(n) = A187907(n) for n=1..20; A187232(21)=39 and A187907(21)=40.

Cf. A187224, A187908.

r=4-5^(1/2);
seqA = Table[Floor[r*n], {n, 1, 220}] (* A187330 *)
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]] (* A187907 *)
Complement[Range[Length[seqA]], limseqU]  (* A187908 *)
(* Peter J. C. Moses, Mar 15 2011 *)

makelist(floor((4-sqrt(5))*n),n,1,100); /* Martin Ettl, Oct 17 2012 */

cp's OEIS Frontend

A187339 a(n) = floor((7+sqrt(5))*n/4); complement of A187330.

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