OFFSET
1,1
COMMENTS
Dahlenberg & Edgar proved that this sequence is infinite and that there are no consecutive runs of 5 or more factorial base Niven numbers.
a(1)-a(18) were calculated by Dahlenberg & Edgar.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..512
Paul Dahlenberg and Tom Edgar, Consecutive factorial base Niven numbers, Fibonacci Quarterly, Vol. 56, No. 2 (2018), pp. 163-166; alternative link. [Wayback Machine link]
EXAMPLE
MATHEMATICA
sf[n_] := Module[{s = 0, i = 2, k = n}, While[k > 0, k = Floor[n/i!]; s = s + (i - 1)*k; i++]; n - s]; fnQ[n_] := Divisible[n, sf[n]]; aQ[n_] := AllTrue[n + Range[0, 3], fnQ]; Select[Range[10^8], aQ] (* after Jean-François Alcover at A034968 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Oct 07 2019
STATUS
approved