A060495 Each permutation in the list A060117 converted to Site Swap notation, with "zero throws" (fixed elements) replaced with n, the length of siteswap.

1, 11, 312, 111, 231, 222, 4413, 1313, 4112, 1111, 2411, 2312, 4242, 1241, 4233, 1223, 2222, 2231, 3441, 3342, 3131, 3122, 3423, 3333, 55514, 14514, 51414, 11314, 25314, 24414, 55113, 14113, 51112, 11111, 25111, 24112, 52512, 12511, 52413

Offset: 0

Author

Antti Karttunen, Mar 21 2001

Keywords

• nonn
• base

Comments

This sequence is not well-defined for n >= 3628800 because the Site Swap notation can contain values exceeding 9, for example, the Site Swap notation for a(3628800) is [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10]. - Sean A. Irvine, Nov 25 2022

Links

• Site Swap notation explained.

Crossrefs

Cf. factorial base representation A007623 and A060496, A006694.

See also A060498, A060499, A061417. Average of digits gives number of balls: A060501.

Programs

Maple

Perm2SiteSwap1 := proc(p) local ip,n,i,a; n := nops(p); ip := convert(invperm(convert(p,'disjcyc')),'permlist',n); a := []; for i from 1 to n do a := [op(a),((ip[i]-i) mod n)]; od; RETURN(a); end;
SiteSwap1ToDec := proc(s) local i,z,n; n := nops(s); z := 0; for i from 1 to n do z := 10*z; if(0 = s[i]) then z := z+n; else z := z+s[i]; fi; od; RETURN(z); end;

Formula

a(n) = SiteSwap1ToDec(Perm2SiteSwap1(PermUnrank3R(n))).