A221617 - OEIS

A221617

Number of 12-hour periods after which the (27+n) balls of a ball clock return to their initial state.

25, 27, 84, 380, 138, 24, 180, 140, 330, 627, 1190, 200, 252, 420, 399, 1020, 6160, 74, 148, 360, 47, 5460, 870, 1160, 748, 1508, 680, 147, 1260, 1596, 1092, 3220, 140, 57, 270, 2436, 440, 840, 62, 177, 1260, 840, 54, 4641, 244, 21840, 228, 644, 1320, 3795, 1980, 4620, 2976, 34410, 12012, 550, 5700, 12243, 1155, 120120, 249

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OFFSET

0,1

COMMENTS

The clock has 3 bars with lengths 5, 11, 11. So the minimal number of balls is (5+11+11) + 1 = 27. But it can also operate with more balls, hence the (27+n) in sequence name.

To get the above data, first call PARI script clock() (A221616) with n = 0, 1, ..., and send the result into the orderp() script below. The order of a permutation is computed with the LCM of cycle sizes.

LINKS

Table of n, a(n) for n=0..60.

ACM International Collegiate Programming Contest, 1995 ACM-ICPC World Finals Problems

Jim Weigang, Ball Clock Problem

PROG

(PARI) orderp(v) = {nv = length(v); vbp = vector(nv); ordr = 1; for (i=1, nv, if (vbp[i] == 0, cpt = 0; j = i; while (vbp[j] == 0, nextj = v[j]; vbp[j] = 1; j = nextj; cpt++; ); ordr = lcm(ordr, cpt); ); ); return(ordr); }

CROSSREFS

Cf. A221616.

Sequence in context: A096522 A195351 A015734 * A083806 A239521 A345509

Adjacent sequences: A221614 A221615 A221616 * A221618 A221619 A221620

KEYWORD

nonn

AUTHOR

Michel Marcus, Jan 21 2013

STATUS

approved