A088438 A chaotic Cantor integer type product set of the factorial function that trifurcates.

2, 6, 4, 7, 24, 35, 8, 18, 70, 88, 12, 29, 140, 165, 16, 40, 234, 266, 20, 52, 352, 391, 24, 64, 494, 540, 28, 76, 660, 713, 32, 88, 850, 910, 36, 99, 1064, 1131, 40, 111, 1302, 1376, 44, 123, 1564, 1645, 48, 135, 1850, 1938, 52, 147, 2160, 2255, 56, 159, 2494

Offset: 0

Author

Roger L. Bagula, Nov 09 2003

Keywords

• nonn
• uned

Comments

This result is due to analysis of the prime product, composite product and factorial type function to a more general type of function: n!=Product[Set1[i],{i, limit1, limit2}]*Product[Set2[i],{i,limit3,limit4}] In this case the second product contains two intervals instead of one.

Crossrefs

Cf. A088140.

Programs

Mathematica

(* factorial based function with half interval Cantor hole in the middle*) p[n_]=n!/Product[i, {i, n-Floor[n/4], n-Floor[3*n/4]}] digits=200 a0=Table[Floor[p[n]/p[n-1]], {n, 2, digits}]

Formula

P[n]=n!/Product[i, {i, n-Floor[n/4], n-Floor[3*n/4]}] a(n) = Floor[P[n]/P[n-1]]