A046148 Number of n-digit numbers with maximal multiplicative persistence A014553.
10, 1, 9, 12, 20, 2430, 5229, 7448, 282852, 88200, 8015040, 200676960, 2701775518, 24655323238, 15765750, 1715313600, 59049874884, 1112489914536, 14162129381400, 135917876094000, 1050596838951660, 6832549561749912, 38554260751029408, 193081920969057120
Offset: 1
Links
- Giovanni Resta, Table of n, a(n) for n = 1..50
- N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
- Eric Weisstein's World of Mathematics, Multiplicative Persistence.
Programs
-
Mathematica
mper[n_] := Block[{k=0, m=n}, While[m>9, k++; m = Times @@ IntegerDigits@ m]; k]; mxper = {1, 4, 5, 6, 7, 7, 8, 9, 9, 10, 10, 10}; multi[w_] := Total[w]!/Times @@ (w!); a[1]=10; a[n_] := Sum[ Total[ If[ mxper[[n]] == 1 + mper[Times @@ (Range[9]^#)], multi[#], 0] & /@ Permutations[p]], {p, IntegerPartitions[n, {9}, Range[0, n]]}]; Array[a, 12] (* Giovanni Resta, Sep 01 2018 *)
Extensions
a(8)-a(12) from Donovan Johnson, Mar 30 2010
a(13)-a(24) from Giovanni Resta, Aug 31 2018
Comments