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

1,1

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.

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 *)

Crossrefs

Cf. A014553, A046149, A046150.

Sequence in context: A107830 A144261 A337819 * A231933 A164915 A010691

Adjacent sequences: A046145 A046146 A046147 * A046149 A046150 A046151

Keyword

nonn,base

Author

Eric W. Weisstein

Extensions

a(8)-a(12) from Donovan Johnson, Mar 30 2010

a(13)-a(24) from Giovanni Resta, Aug 31 2018

Status

approved