|
%I #12 Aug 25 2023 08:40:40
%S 244,844,1444,1727,5164,5764,5950,10084,10967,13583,15190,20207,21130,
%T 22048,40444,40535,41044,45364,45550,56015,60730,62848,63479,80644,
%U 91408,132208,153340,163799,173008,176110,178007,195983,242368,280852,283168,363004,363604
%N Starts of runs of 3 consecutive factorial base Niven numbers (A118363).
%C Dahlenberg & Edgar proved that this sequence is infinite.
%H Amiram Eldar, <a href="/A328206/b328206.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Dahlenberg and Tom Edgar, <a href="https://www.fq.math.ca/Abstracts/56-2/dalenberg.pdf">Consecutive factorial base Niven numbers</a>, Fibonacci Quarterly, Vol. 56, No. 2 (2018), pp. 163-166; <a href="https://web.archive.org/web/20211018191809/https://community.plu.edu/~edgartj/consecutivefactniven.pdf">alternative link</a>. [Wayback Machine link]
%e 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.
%t 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 *)
%Y Cf. A007623, A034968, A118363.
%K nonn,base
%O 1,1
%A _Amiram Eldar_, Oct 07 2019
|
