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A075317 Pair the odd numbers such that the k-th pair is (r, r+2k) where r is the smallest odd number not included earlier: (1,3),(5,9),(7,13),(11,19),(15,25),(17,29),(21,35),(23,39),(27,45),... This is the sequence of the first member of pairs. 5
1, 5, 7, 11, 15, 17, 21, 23, 27, 31, 33, 37, 41, 43, 47, 49, 53, 57, 59, 63, 65, 69, 73, 75, 79, 83, 85, 89, 91, 95, 99, 101, 105, 109, 111, 115, 117, 121, 125, 127, 131, 133, 137, 141, 143, 147, 151, 153, 157, 159, 163, 167, 169, 173, 175, 179, 183, 185, 189, 193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

(a(n), A075318(n)) = (2A(n)-1, 2B(n)-1), where A and B are the basic Wythoff sequences A(n)=A000201(n) and B(n)=A001950(n). For a proof cf. Section 2 of the Carlitz et al. paper. - Michel Dekking, Sep 05 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations, Fib. Quart. 10 (1972), 1-28.

FORMULA

a(n) = 2*floor(n*phi)-1, where phi=(1+sqrt(5))/2. - Michel Dekking, Sep 05 2016

MAPLE

A075317 := proc(nmax) local r, k, a, pairs ; a := [1] ; pairs := [1, 3] ; k := 2 ; r := 5 ; while nops(a) < nmax do while r in pairs do r := r+2 ; od ; a := [op(a), r] ; if r+2*k in pairs then printf("inconsistency", k) ; fi ; pairs := [op(pairs), r, r+2*k] ; k := k+1 ; od ; RETURN(a) ; end: a := A075317(200) ; for n from 1 to nops(a) do printf("%d, ", op(n, a)) ; od ; # R. J. Mathar, Nov 12 2006

MATHEMATICA

Table[2 Floor[n (1 + Sqrt[5]) / 2] - 1, {n, 80}] (* Vincenzo Librandi, Sep 05 2016 *)

PROG

(MAGMA) [2*Floor(n*(1+Sqrt(5))/2)-1: n in [1..60]]; // Vincenzo Librandi, Sep 05 2016

CROSSREFS

Cf. A075318, A075319, A075320.

Sequence in context: A098243 A037141 A029624 * A134643 A039001 A023741

Adjacent sequences:  A075314 A075315 A075316 * A075318 A075319 A075320

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Sep 14 2002

EXTENSIONS

More terms from R. J. Mathar, Nov 12 2006

STATUS

approved

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Last modified June 25 10:28 EDT 2021. Contains 345453 sequences. (Running on oeis4.)