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A115094 Permutation of N based on lower Wythoff sequence. 0
3, 2, 1, 6, 5, 4, 7, 9, 8, 10, 12, 11, 13, 16, 15, 14, 19, 18, 17, 20, 22, 21, 23, 25, 24, 26, 29, 28, 27, 32, 31, 30, 35, 34, 33, 36, 38, 37, 39, 42, 41, 40, 45, 44, 43, 48, 47, 46, 49, 51, 50, 52, 55, 54, 53, 58, 57, 56, 61, 60, 59, 62, 64, 63, 65, 67, 66, 68, 71, 70, 69, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

(1) a(n)=n if and only if n is in the upper Wythoff sequence, A001950. (2) This is a self-inverse permutation of N. (3) a(n)-n is one of -2,-1,0,1,2 for every n and each of these occurs infinitely many times. (4) The sequence a(n)-n is a nonperiodic tiling of N.

LINKS

Table of n, a(n) for n=1..72.

FORMULA

Let L be the lower Wythoff sequence, A000201. Then a(n)=n if n is not any L(k), a(n)=L(k+1) if n=L(k) for odd k, a(n)=L(k-1) if n=L(k) for even k.

EXAMPLE

a(1)=3=L(1+1) because 1=L(1).

a(2)=2 because 2 is not in L.

a(3)=1=L(2-1) because 3=L(2).

a(4)=6=L(3+1) because 4=L(3).

a(6)=4=L(4-1) because 6=L(4).

CROSSREFS

Cf. A000201, A001950, A002251.

Sequence in context: A194761 A129674 A120771 * A165958 A113655 A177977

Adjacent sequences:  A115091 A115092 A115093 * A115095 A115096 A115097

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 02 2006

STATUS

approved

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Last modified January 22 18:53 EST 2019. Contains 319365 sequences. (Running on oeis4.)