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A328207
Starts of runs of 4 consecutive factorial base Niven numbers (A118363).
11
9320542, 11397166, 29048470, 29394574, 40469902, 40816006, 58467310, 72657574, 84079006, 101730310, 178911502, 200716054, 283088806, 479329774, 485213542, 499403806, 528476542, 530553166, 544743430, 559625902, 559972006, 574162270, 603235006, 617425270, 641652550
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
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
9320542 is in the sequence since 9320542, 9320543, 9320544 and 9320545 are all in A118363: A034968(9320542) = 22 is a divisor of 9320542, A034968(9320543) = 23 is a divisor of 9320543, A034968(9320544) = 18 is a divisor of 9320544, and A034968(9320545) = 19 is a divisor of 9320545.
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