The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A194959

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A194959

Fractalization of (1 + floor(n/2)).
(history; published version)

#51 by N. J. A. Sloane at Wed Oct 14 10:51:20 EDT 2020

STATUS

proposed

approved

#50 by Kevin Ryde at Fri Oct 09 20:45:40 EDT 2020

STATUS

editing

proposed

#49 by Kevin Ryde at Fri Oct 09 20:44:27 EDT 2020

CROSSREFS

Cf. A003558 (g permutation order), A102417 (index), A330081 (on bits), A057058 (inverse).

STATUS

proposed

editing

#48 by Kevin Ryde at Fri Oct 09 19:41:14 EDT 2020

STATUS

editing

proposed

#47 by Kevin Ryde at Fri Oct 09 19:32:06 EDT 2020

FORMULA

Fixed points: T(n,k)=k for k=1, and k = (2/3)*(n+1) when an integer. [Lévy, chapter 1 section 2 equation (3)]

Discussion

Fri Oct 09

19:41

Kevin Ryde: As a note on xref A102417, its name refers to permutations of 1..n listed in lexicographic order, index into that list (Pari permtonum() style).

#46 by Kevin Ryde at Fri Oct 09 19:29:24 EDT 2020

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FractalSequence.html">Fractal sequence</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Interspersion.html">Interspersion</a>

MathWorld, <a href="http://mathworld.wolfram.com/FractalSequence.html">Fractal sequence</a>

MathWorld, <a href="http://mathworld.wolfram.com/Interspersion.html">Interspersion</a>

#45 by Kevin Ryde at Fri Oct 09 19:27:33 EDT 2020

FORMULA

(End)

From Kevin Ryde, Oct 09 2020: (Start)

T(n,k) = 2*k-1 if 2*k-1 <= n, or 2*(n+1-k) if 2*k-1 > n. [Lévy, chapter 1 section 1 equations (a),(b)]

Fixed points: T(n,k)=k for k=1, and k = (2/3)*(n+1) when an integer. [Lévy, chapter 1 section 2 equation (3)]

T(n,k) = 2*k-1 if 2*k-1 <= n, or 2*(n+1-k) if 2*k-1 > n. [Lévy, chapter 1 section 1 equations (a),(b)] - Kevin Ryde, Oct 09 2020

#44 by Kevin Ryde at Fri Oct 09 19:15:37 EDT 2020

LINKS

Paul Lévy, <a href="http://www.numdam.org/item?id=CM_1951__8__1_0">Sur quelques classes de permutations</a>, Compositio Mathematica, Volume 8, 1951, pages 1-48. P_n = g(n).

FORMULA

T(n,k) = 2*k-1 if 2*k-1 <= n, or 2*(n+1-k) if 2*k-1 > n. [Lévy, chapter 1 section 1 equations (a),(b)] - Kevin Ryde, Oct 09 2020

PROG

(PARI) T(n, k) = min(k<<1-1, (n-k+1)<<1); \\ Kevin Ryde, Oct 09 2020

CROSSREFS

Cf. A003558 (g permutation order), A102417 (index), A057058 (inverse).

STATUS

approved

editing

#43 by N. J. A. Sloane at Thu Aug 23 17:16:29 EDT 2018

STATUS

proposed

approved

#42 by Jon E. Schoenfield at Tue Jul 10 21:15:55 EDT 2018

STATUS

editing

proposed