A108517 Numbers m such that the permutation of the first m natural numbers R_m(n)=if(1<=n<m-pi(m), c(n), if(n=m, 1, prime(n-m-pi(m)+1))) is a cyclic permutation where c(k) is the k-th composite number(for each natural number k, c(k)=A002808(k)).

1, 15, 33, 66, 85, 112, 125, 148, 213, 237, 321, 381, 466, 518, 585, 637, 956, 2127, 2571, 4255, 4884, 6686, 9193, 10412, 11073

Offset

1,2

Comments

All the 24 known terms of this sequence are nonprimes. Is this true in general?

Links

Table of n, a(n) for n=1..25.

Example

If m>3 & pi(m)=k then for n=1,2,...,m S_m(n) are respectively
c(1),c(2),...,c(m-k-1),prime(1),prime(2),...,prime(k),1.
33 is in the sequence because R_33=(1, 4, 9, 16, 26, 11, 20, 32, 31, 29, 19, 30, 23, 3, 8, 15, 25, 7, 14, 24, 5, 10, 18, 18, 28, 17, 27, 13, 22, 2, 6, 12, 21, 33) is a cyclic permutation.

Mathematica

(f[n_] := (a = Table[Prime[k], {k, PrimePi[n]}]; b = Complement [Range[2, n], a]; c = Join[b, a, {1}]); d[n_, m_] := f[n][[m]]; g[r_] := (v = {1}; d[m_] := d[r, m]; For[t = 1, !MemberQ[v, d[v[[ -1]]]] && t < r, v = Append[v, d[v[[ -1]]]]; t++ ]; t); Do[If[ !PrimeQ[r] && r == g[r], Print[r]], {r, 10800}])

Crossrefs

Cf. A002808, A108515, A108516.

Sequence in context: A228318 A228321 A277385 * A211327 A222179 A322493

Adjacent sequences: A108514 A108515 A108516 * A108518 A108519 A108520

Keyword

more,nonn

Author

Farideh Firoozbakht, Jul 03 2005

Status

approved