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A075318 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 second member of pairs. 5
3, 9, 13, 19, 25, 29, 35, 39, 45, 51, 55, 61, 67, 71, 77, 81, 87, 93, 97, 103, 107, 113, 119, 123, 129, 135, 139, 145, 149, 155, 161, 165, 171, 177, 181, 187, 191, 197, 203, 207, 213, 217, 223, 229, 233, 239, 245, 249, 255, 259, 265, 271, 275, 281, 285, 291, 297 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

(A075317(n),a(n)) = (2*A(n)-1, 2*B(n)-1), where A and B are the basic Wythoff sequences A(n)=A000201(n) and B(n)=A001950(n). For a proof, see section 2 of the Carlitz et al. paper. - Michel Dekking, Sep 08 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^2)-1, where phi=(1+sqrt(5))/2. - Michel Dekking, Sep 08 2016

MAPLE

A075318 := proc(nmax) local r, k, a, pairs ; a := [3] ; pairs := [1, 3] ; k := 2 ; r := 5 ; while nops(a) < nmax do while r in pairs do r := r+2 ; od ; if r+2*k in pairs then printf("inconsistency", k) ; fi ; a := [op(a), r+2*k] ; pairs := [op(pairs), r, r+2*k] ; k := k+1 ; od ; RETURN(a) ; end: a := A075318(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)^2] - 1, {n, 60}] (* Vincenzo Librandi, Sep 08 2016 *)

PROG

(MAGMA) [2*Floor(n*((1+Sqrt(5))/2)^2)-1: n in [1..60]]; // Vincenzo Librandi, Sep 08 2016

(PARI) a(n)=localbitprec(logint(sqrtint(45*n^4)+5*n^2, 2)+2); 2*floor(n*(sqrt(5)+1)/2+n)-1 \\ Charles R Greathouse IV, Sep 09 2016

CROSSREFS

Cf. A075317, A075319, A075320.

Sequence in context: A032415 A268044 A190745 * A171101 A287184 A197569

Adjacent sequences:  A075315 A075316 A075317 * A075319 A075320 A075321

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Sep 14 2002

EXTENSIONS

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

STATUS

approved

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Last modified November 21 22:16 EST 2019. Contains 329383 sequences. (Running on oeis4.)