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A328206
Starts of runs of 3 consecutive factorial base Niven numbers (A118363).
16
244, 844, 1444, 1727, 5164, 5764, 5950, 10084, 10967, 13583, 15190, 20207, 21130, 22048, 40444, 40535, 41044, 45364, 45550, 56015, 60730, 62848, 63479, 80644, 91408, 132208, 153340, 163799, 173008, 176110, 178007, 195983, 242368, 280852, 283168, 363004, 363604
OFFSET
1,1
COMMENTS
Dahlenberg & Edgar proved that this sequence is infinite.
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
244 is in the sequence since 244, 245 and 246 are in A118363. A034968(244) = 4 is a divisor of 244, A034968(245) = 5 is a divisor of 245, and A034968(246) = 3 is a divisor of 246.
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, 2], fnQ]; Select[Range[400000], aQ] (* after Jean-François Alcover at A034968 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Oct 07 2019
STATUS
approved